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One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

One of the reasons linear motors, a technology nearly a century old, have not been adopted for a large number of linear motion applications is that they have historically had poor efficiencies. This has restricted the progress of linear motor development. The concept of a linear motor as a rotary motor cut and laid out flat with a conventional rotary motor control scheme as a design basis may not be the best way to design and control a high-speed linear motor. End effects and other geometry subtleties of a linear motor make it unique, and a means of optimizing efficiency with both the motor geometry and the motor control scheme will be analyzed to create a High-Speed Linear Induction Motor (LIM) with a higher efficiency than what is possible with conventional motors and controls. This thesis pursues the modeling of a short secondary type Double-Sided Linear Induction Motor (DSLIM) that is proposed for use as an Electromagnetic Aircraft Launch System (EMALS) aboard the CVN-2 1. Mathematical models for the prediction of effects that are peculiar to DSLIM are formulated, and their overall effects on the performance of the proposed machine are analyzed. These effects are used to generate a transient motor model, which is then driven by a motor controller that is specifically designed to the characteristics of the proposed DSLIM. Due to this DSLIM's role as a linear accelerator, the overall efficiency of the DSLIM will be judged by the kinetic energy of the launched projectile versus the total electric energy that the machine consumes. This thesis is meant to propose a maximum possible efficiency for a DSLIM in this type of role.

We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the metric induced by the noise. The long term stochastic dynamics on the manifold will be completely characterized by the long term density $\rho$ and the long term current density $J$. As such, control problems may be reformulated as variational problems over $\rho$ and $J$. We discuss several optimization problems: the problem in which both $\rho$ and $J$ are varied freely, the problem in which $\rho$ is fixed and the one in which $J$ is fixed. These problems lead to different kinds of operator problems: linear PDEs in the first two cases and a nonlinear PDE in the latter case. These results are obtained through through variational principle using infinite dimensional Lagrange multipliers. In the case where the initial dynamics are reversible we obtain the result that the optimally controlled diffusion is also symmetrizable. The particular case of constraining the dynamics to be reversible of the optimally controlled process leads to a linear eigenvalue problem for the square root of the density process.

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.

In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art SMT solvers, in particular in the domain of SW and HW verification. Many SMT-encodable problems of interest, however, require also the capability of finding models that are optimal wrt. some cost functions. In previous work, namely "Optimization Modulo Theory with Linear Rational Cost Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the minimization of cost functions on linear arithmetic over the rationals, by means of a combination of SMT and LP minimization techniques. In this paper we push the envelope of our OMT approach along three directions: first, we extend it to work also with linear arithmetic on the mixed integer/rational domain, by means of a combination of SMT, LP and ILP minimization techniques; second, we develop a multi-objective version of OMT, so that to handle many cost functions simultaneously; third, we develop an incremental version of OMT, so that to exploit the incrementality of some OMT-encodable problems. An empirical evaluation performed on OMT-encoded verification problems demonstrates the usefulness and efficiency of these extensions.

In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS$_\varepsilon$) and least squares boosting (LS-Boost($\varepsilon$)), can be viewed as subgradient descent to minimize the loss function defined as the maximum absolute correlation between the features and residuals. We also propose a modification of FS$_\varepsilon$ that yields an algorithm for the Lasso, and that may be easily extended to an algorithm that computes the Lasso path for different values of the regularization parameter. Furthermore, we show that these new algorithms for the Lasso may also be interpreted as the same master algorithm (subgradient descent), applied to a regularized version of the maximum absolute correlation loss function. We derive novel, comprehensive computational guarantees for several boosting algorithms in linear regression (including LS-Boost($\varepsilon$) and FS$_\varepsilon$) by using techniques of modern first-order methods in convex optimization. Our computational guarantees inform us about the statistical properties of boosting algorithms. In particular they provide, for the first time, a precise theoretical description of the amount of data-fidelity and regularization imparted by running a boosting algorithm with a prespecified learning rate for a fixed but arbitrary number of iterations, for any dataset.

We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the past 10-15 years, we present a Mixed Integer Linear Optimization (MILO) approach to obtain certifiably optimal global solutions to this nonconvex optimization problem. The current state of algorithmics in integer optimization makes our proposal substantially more computationally attractive than the least squares subset selection framework based on integer quadratic optimization, recently proposed in [8] and the continuous nonconvex quadratic optimization framework of [33]. We propose new discrete first-order methods, which when paired with state-of-the-art MILO solvers, lead to good solutions for the Discrete Dantzig Selector problem for a given computational budget. We illustrate that our integrated approach provides globally optimal solutions in significantly shorter computation times, when compared to off-the-shelf MILO solvers. We demonstrate both theoretically and empirically that in a wide range of regimes the statistical properties of the Discrete Dantzig Selector are superior to those of popular $\ell_{1}$-based approaches. We illustrate that our approach can handle problem instances with p = 10,000 features with certifiable optimality making it a highly scalable combinatorial variable selection approach in sparse linear modeling.

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization problems. Methods in the APS class include many well-known algorithms such as the proximal splitting method (PSM), the block coordinate descent method (BCD) and the approximate gradient projection methods for smooth convex optimization. We establish the linear convergence of APS methods under a local error bound assumption. Since the latter is known to hold for compressive sensing and sparse group LASSO problems, our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.

Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We define a cone projection problem using the data of a given linear vector optimization problem and consider the problem to determine the extreme directions and a basis of the lineality space of the projected cone $K$. The result of this problem yields a solution of the linear vector optimization problem. Analogously, the dual cone projection problem is related to the polar cone of $K$: One obtains a solution of the geometric dual linear vector optimization problem. We sketch the idea of a resulting algorithm for solving arbitrary linear vector optimization problems and provide an alternative proof of the geometric duality theorem based on duality of polytopes.

The main result of the paper shows that, for 1

A new optimization method for the design of nearly linear-phase IIR digital filters that satisfy prescribed specifications is proposed. The group-delay deviation is minimized under the constraint that the passband ripple and stopband attenuation are within the prescribed specifications and either a prescribed or an optimized group delay can be achieved. By representing the filter in terms of a cascade of second-order sections, a non-restrictive stability constraint characterized by a set of linear inequality constraints can be incorporated in the optimization algorithm. An additional feature of the method, which is very useful in certain applications, is that it provides the capability of constraining the maximum gain in transition bands to be below a prescribed level. Experimental results show that filters designed using the proposed method have much lower group-delay deviation for the same passband ripple and stopband attenuation when compared with corresponding filters designed with several state-of-the-art competing methods.

In this paper, we proposed a matrix-free double-search direction based on the updated parameter file of the double-search direction with a new mathematical formula for the gamma parameter. When comparing the numerical results of this algorithm with the standard (HWY) algorithm which given by Halilu, Waziri and Yusuf in 2020. We get very robust numerical results. The proposed algorithm is devoid of derivatives to solve large-scale non-linear problems by combining two search directions in one search direction. We demonstrated the overall convergence of the proposed algorithm under certain conditions. The numerical results presented in this paper show that the new search direction is useful for solving widespread non-linear test problems.

In this paper we provide a complementary set of results to those we present in our companion work \cite{Stojnicl1HidParasymldp} regarding the behavior of the so-called partial $\ell_1$ (a variant of the standard $\ell_1$ heuristic often employed for solving under-determined systems of linear equations). As is well known through our earlier works \cite{StojnicICASSP10knownsupp,StojnicTowBettCompSens13}, the partial $\ell_1$ also exhibits the phase-transition (PT) phenomenon, discovered and well understood in the context of the standard $\ell_1$ through Donoho's and our own works \cite{DonohoPol,DonohoUnsigned,StojnicCSetam09,StojnicUpper10}. \cite{Stojnicl1HidParasymldp} goes much further though and, in addition to the determination of the partial $\ell_1$'s phase-transition curves (PT curves) (which had already been done in \cite{StojnicICASSP10knownsupp,StojnicTowBettCompSens13}), provides a substantially deeper understanding of the PT phenomena through a study of the underlying large deviations principles (LDPs). As the PT and LDP phenomena are by their definitions related to large dimensional settings, both sets of our works, \cite{StojnicICASSP10knownsupp,StojnicTowBettCompSens13} and \cite{Stojnicl1HidParasymldp}, consider what is typically called the asymptotic regime. In this paper we move things in a different direction and consider finite dimensional scenarios. Basically, we provide explicit performance characterizations for any given collection of systems/parameters dimensions. We do so for two different variants of the partial $\ell_1$, one that we call exactly the partial $\ell_1$ and another one, possibly a bit more practical, that we call the hidden partial $\ell_1$.

For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of network codes in terms of the number of flows allowed to be coded together, and are not entirely distributed. In this paper, we consider a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of edge use based on mixing. We first formulate the minimumcost network coding design problem. To solve the optimization problem, we propose two equivalent alternative formulations with discrete mixing and continuous mixing, respectively, and develop distributed algorithms to solve them. Our approach allows fairly general coding across flows and guarantees no greater cost than any solution without network coding.

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.

We present a review and bibliography of the main results obtained during a research on ABS (Abaffy, Broyden, Spedicato) methods.

The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the AD-ADMM on a high-performance computer cluster by solving a large-scale logistic regression problem.

In the classic multi-armed bandits problem, the goal is to have a policy for dynamically operating arms that each yield stochastic rewards with unknown means. The key metric of interest is regret, defined as the gap between the expected total reward accumulated by an omniscient player that knows the reward means for each arm, and the expected total reward accumulated by the given policy. The policies presented in prior work have storage, computation and regret all growing linearly with the number of arms, which is not scalable when the number of arms is large. We consider in this work a broad class of multi-armed bandits with dependent arms that yield rewards as a linear combination of a set of unknown parameters. For this general framework, we present efficient policies that are shown to achieve regret that grows logarithmically with time, and polynomially in the number of unknown parameters (even though the number of dependent arms may grow exponentially). Furthermore, these policies only require storage that grows linearly in the number of unknown parameters. We show that this generalization is broadly applicable and useful for many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weight matching, shortest path, and minimum spanning tree computations.

Linear and nonlinear entanglement witnesses for a given bipartite quantum systems are constructed. Using single particle feasible region, a way of constructing effective entanglement witnesses for bipartite systems is provided by exact convex optimization. Examples for some well known two qutrit quantum systems show these entanglement witnesses in most cases, provide necessary and sufficient conditions for separability of given bipartite system. Also this method is applied to a class of bipartite qudit quantum systems with details for d=3, 4 and 5. Keywords: non-linear and linear entanglement witnesses PACS number(s): 03.67.Mn, 03.65.Ud

Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which the decision variables are matrices running over certain feasible matrix sets, while the ranks and inertias of the variable matrices are taken as integer-valued objective functions. In this paper, we establish a group of explicit formulas for calculating the maximal and minimal values of the rank- and inertia-objective functions of the Hermitian matrix expression $A_1 - B_1XB_1^{*}$ subject to the linear matrix inequality $B_2XB_2^{*} \succcurlyeq A_2$ $(B_2XB_2^{*} \preccurlyeq A_2)$ in the L\"owner partial ordering, and give applications of these formulas in characterizing behaviors of some constrained matrix-valued functions.

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. The standard benchmark is the loss of the best strategy chosen from a bounded comparator set. When the the comparison set and the adversary's gradients satisfy L_infinity bounds, we give the value of the game in closed form and prove it approaches sqrt(2T/pi) as T -> infinity. Interesting algorithms result when we consider soft constraints on the comparator, rather than restricting it to a bounded set. As a warmup, we analyze the game with a quadratic penalty. The value of this game is exactly T/2, and this value is achieved by perhaps the simplest online algorithm of all: unprojected gradient descent with a constant learning rate. We then derive a minimax-optimal algorithm for a much softer penalty function. This algorithm achieves good bounds under the standard notion of regret for any comparator point, without needing to specify the comparator set in advance. The value of this game converges to sqrt{e} as T ->infinity; we give a closed-form for the exact value as a function of T. The resulting algorithm is natural in unconstrained investment or betting scenarios, since it guarantees at worst constant loss, while allowing for exponential reward against an "easy" adversary.

The linear programming (LP) is one of the most popular necessary optimization tool used for data analytics as well as in various scientific fields. However, the current state-of-art algorithms suffer from scalability issues when processing Big Data. For example, the commercial optimization software IBM CPLEX cannot handle an LP with more than hundreds of thousands variables or constraints. Existing algorithms are fundamentally hard to scale because they are inevitably too complex to parallelize. To address the issue, we study the possibility of using the Belief Propagation (BP) algorithm as an LP solver. BP has shown remarkable performances on various machine learning tasks and it naturally lends itself to fast parallel implementations. Despite this, very little work has been done in this area. In particular, while it is generally believed that BP implicitly solves an optimization problem, it is not well understood under what conditions the solution to a BP converges to that of a corresponding LP formulation. Our efforts consist of two main parts. First, we perform a theoretic study and establish the conditions in which BP can solve LP [1,2]. Although there has been several works studying the relation between BP and LP for certain instances, our work provides a generic condition unifying all prior works for generic LP. Second, utilizing our theoretical results, we develop a practical BP-based parallel algorithms for solving generic LPs, and it shows 71x speed up while sacrificing only 0.1 accuracy compared to the state-of-art exact algorithm. As a result of the study, the PIs have published two conference papers and two follow-up journal papers are under submission. We refer the readers to our published work for details.

Nowadays, Vehicular Ad-Hoc Network (VANET) has got more attention from the researchers. The researchers have studied numerous topics of VANET, such as the routing protocols of VANET and the MAC protocols of VANET. The aim of their works is to improve the network performance of VANET, either in terms of energy consumption or packet delivery ratio (PDR) and delay. For this research paper, the main goal is to find the coefficient of a, b and c of three non-linear equations by using a NewtonRaphson method. Those three non-linear equations are derived from a different value of Medium Access Control (MAC) protocol's parameters. After that, those three coefficient is then will be used in optimization of the VANET in terms of energy, PDR, and delay.

Within general pattern for the branch and bound method, the solution algorithm of integer optimization in case of the linear-fractional objective function and additional linear constraints is considered in the articl

Within general pattern for the branch and bound method, the solution algorithm of integer optimization in case of the linear-fractional objective function and additional linear constraints is considered in the articl

Within general pattern for the branch and bound method, the solution algorithm of integer optimization in case of the linear-fractional objective function and additional linear constraints is considered in the articl

No Abstract Available

Our work is developed in context of studing Massive MIMO in a 5G context. The aim is to optimize spectral efficiency of several users hyper MIMO system during Uplink communication in a multi-cell contaminated pilot environment, using a new type of precoders called single cell-minimum mean square eroor (S-MMSE) and multicell-minimum mean square eroor (MMMSE). Indeed, we address two key and well-known issues of massive multiuser MIMO (MU-MIMO) environments in a test-driven development (TDD) operation scheme, namely acquisition of uplink channel state information (UL) and optimisation of the bit stream per unit frequency, the spectral efficiency (SE). From a practical point of view, these two notions are inclusively linked. Indeed, a very good channel estimation leads to a better spectral efficiency. In our approcah, we derive from the minimum mean square error estimator (MMSE) to two new types of precoders that can operate in a multicell environment with a contaminated pilot sequence, namely the SMMSE and the M-MMSE. A comparative study performance of these classical precoders such as regulated zero forcing (RZF), ZF (Zero Forcing) and MR (Minimum Ratio) encountered in multi-antenna processing shows an improvement of nearly 51% in terms of system gain and spectral efficiency.

Development and acquisition of naval communication, data, and radar systems for ships is an almost entirely modular process. For this reason, virtually all existing systems have separate controllers, antennas, and transmitters. However, future systems could use existing planar antennas that operate across a range of frequencies and create a variety of complex waveforms, eliminating the need to develop separate antennas and transmitters. Additionally, frequency use plans are expensive in terms of time and effort to develop and change. The Integrated Topside (InTop) joint Navy industry open architecture study published in 2010 described the need for an integrated sensor and communication system that is modular, scalable, and capable of performing multiple functions. Such a system requires a scheduling and frequency deconfliction tool that is capable of representing the current antenna configuration and matches those capabilities with requests for frequency space and time. This thesis describes SPECTRA, an integer linear program that can prioritize and optimize the scheduling of available antennas to deconflict time, frequencies, systems and capabilities. It can be uniquely tailored to any platform including naval warships, aircraft, and ground sites.

We present a fully detailed and highly performing implementation of the Linear Method [J. Toulouse and C. J. Umrigar (2007)] to optimize Jastrow-Feenberg and Backflow Correlations in many-body wave-functions, which are widely used in condensed matter physics. We show that it is possible to implement such optimization scheme performing analytical derivatives of the wave-function with respect to the variational parameters achieving the best possible complexity O(N^3) in the number of particles N.

Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

To assess the degree of practical implementation of the optimization principle when comparing options for plans compiled in different ways, this paper proposes a comprehensive indicator of the effectiveness of planned calculations. The advantage of the indicator is that its value is proportional to the magnitude of potential losses from incomplete and incomplete use of available resources, that is, those factors that symbolize the loss of resources in the economic planning process, but have not yet served as criteria for the quality of planning decisions. Therefore, the fact that the optimization method makes it possible to improve (reduce) the value of these indicators with the same volumes of available production resources allows us to conclude that the structural optimization method is very effective and promising in solving production problems of linear programming and in the process of economic planning.

AD480934

A mixed-integer linear programming formulation is developed for minimizing delay to traffic in a signal controlled road network. Offsets, splits of green time and a common cycle time for the network are considered as decision variables simultaneously. The traffic flow pattern is modeled as a periodic platoon, and a link performance function is derived in the form of a piecewise linear convex surface representing the delay incurred by these platoons. Stochastic effects are accounted for by a saturation deterrence function representing the expected overflow queue on each link and are included as an additive component in the objective function. Computational results, using the MPSX system, are given for an arterial with 11 signals in Waltham, Mass., and a portion of the UTCS network in Washington, D.C. containing 20 nodes, 63 links and 21 loops.

Two results are proven: (1) If a certain restricted problem of first-order error analysis in linear programming (specified below), for errors in only the criterion function, has a polynomial-time algorithm, then so does the tautology problem; (2) If the tautology problem is decidable in polynomial time, then linear programs can be solved optimally in polynomial time.

The typical ping control objective for a multistatic network is to optimize a sonar performance metric within a search area over the mission scenario time horizon subject to available ping energy at sources. Assuming sonar performance models and near real-time multistatic target trackers are available sonar performance metric predictions for near-future time window can be obtained. However, for Anti-Submarine Warfare applications, it is not realistic to accurately predict performance metrics involving an unknown number of evasive targets over a long scenario time horizon. Therefore, effective and efficient ping control methods must consider effective strategies to obtain desired performance over the spectrum of operational objectives and time frames. In this paper, we develop four integer-linear goal programming models to provide intelligent ping control decisions for various operational modes that depend on remaining ping energy and remaining scenario time. We incorporate the multiple objectives of: maximizing the sonar performance metric, judicious use of energy-limited sources and maintaining a certain level of ping activity. We show that the constraint matrix of each relaxed linear model possesses the total unimodularity property guaranteeing optimal integer ping control solutions. Therefore computationally efficient linear programming methods can be used in the implementation of these models. We simulate multiple operational scenarios and demonstrate the properties of the resulting ping strategies in terms of the performance metric and individual source and network lifetime. Results are compared to the baseline ping strategy, which considers the sonar performance metric alone.

The typical ping control objective for a multistatic network is to optimize a sonar performance metric within a search area over the mission scenario time horizon subject to available ping energy at sources. Assuming sonar performance models and near real-time multistatic target trackers are available sonar performance metric predictions for near-future time window can be obtained. However, for Anti-Submarine Warfare applications, it is not realistic to accurately predict performance metrics involving an unknown number of evasive targets over a long scenario time horizon. Therefore, effective and efficient ping control methods must consider effective strategies to obtain desired performance over the spectrum of operational objectives and time frames. In this paper, we develop four integer-linear goal programming models to provide intelligent ping control decisions for various operational modes that depend on remaining ping energy and remaining scenario time. We incorporate the multiple objectives of: maximizing the sonar performance metric, judicious use of energy-limited sources and maintaining a certain level of ping activity. We show that the constraint matrix of each relaxed linear model possesses the total unimodularity property guaranteeing optimal integer ping control solutions. Therefore computationally efficient linear programming methods can be used in the implementation of these models. We simulate multiple operational scenarios and demonstrate the properties of the resulting ping strategies in terms of the performance metric and individual source and network lifetime. Results are compared to the baseline ping strategy, which considers the sonar performance metric alone.

This paper deals with a method of optimizing the free coefficients in the characteristic equation of a linear feedback control system. The optimization is carried out by minimizing an index of performance associated with the system's response to a given test disturbance. The index of performance is the integral of a quadratic function of the system state variables. The structure of the index rests upon a logical interpretation of the regulator nature of the control problem. The index for an tr— order system contains n I'll weighting factors whose values are determined from an n-~- order model system. This determination is such that the optimization of a completely free system will yield the model system. A system with fewer than n degrees of freedom in the state variable feedbacks may be optimized with respect to the free feedback coefficients, yielding a system whose dynamic response to a given disturbance is, for this optimization scheme, a best approximation to that of the model. Examples are presented for illustration of the salient features of the method. It is also shown by example that systems with closed- loop zeros may be optimized by this method. The author wishes to thank Dr. Harold A. Titus for his guidance in this investigation.

This paper deals with a method of optimizing the free coefficients in the characteristic equation of a linear feedback control system. The optimization is carried out by minimizing an index of performance associated with the system's response to a given test disturbance. The index of performance is the integral of a quadratic function of the system state variables. The structure of the index rests upon a logical interpretation of the regulator nature of the control problem. The index for an tr— order system contains n I'll weighting factors whose values are determined from an n-~- order model system. This determination is such that the optimization of a completely free system will yield the model system. A system with fewer than n degrees of freedom in the state variable feedbacks may be optimized with respect to the free feedback coefficients, yielding a system whose dynamic response to a given disturbance is, for this optimization scheme, a best approximation to that of the model. Examples are presented for illustration of the salient features of the method. It is also shown by example that systems with closed- loop zeros may be optimized by this method. The author wishes to thank Dr. Harold A. Titus for his guidance in this investigation.

This paper deals with a method of optimizing the free coefficients in the characteristic equation of a linear feedback control system. The optimization is carried out by minimizing an index of performance associated with the system's response to a given test disturbance. The index of performance is the integral of a quadratic function of the system state variables. The structure of the index rests upon a logical interpretation of the regulator nature of the control problem. The index for an tr— order system contains n I'll weighting factors whose values are determined from an n-~- order model system. This determination is such that the optimization of a completely free system will yield the model system. A system with fewer than n degrees of freedom in the state variable feedbacks may be optimized with respect to the free feedback coefficients, yielding a system whose dynamic response to a given disturbance is, for this optimization scheme, a best approximation to that of the model. Examples are presented for illustration of the salient features of the method. It is also shown by example that systems with closed- loop zeros may be optimized by this method. The author wishes to thank Dr. Harold A. Titus for his guidance in this investigation.

Single ions held in linear Paul traps are promising candidates for a future quantum computer. Here, we discuss a two-layer microstructured segmented linear ion trap. The radial and axial potentials are obtained from numeric field simulations and the geometry of the trap is optimized. As the trap electrodes are segmented in the axial direction, the trap allows the transport of ions between different spatial regions. Starting with realistic numerically obtained axial potentials, we optimize the transport of an ion such that the motional degrees of freedom are not excited, even though the transport speed far exceeds the adiabatic regime. In our optimization we achieve a transport within roughly two oscillation periods in the axial trap potential compared to typical adiabatic transports that take of the order 100 oscillations. Furthermore heating due to quantum mechanical effects is estimated and suppression strategies are proposed.