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The talk focuses on expander graphs in conjunction with the combined use of SDPs and eigenvalue techniques for approximating optimal solutions to combinatorial optimization problems. In the first part of the talk I will explain how to construct cost-effective, expanding networks by using 'local' sparsifiers of graphs that emerge as a solution to a semidefinite program. In the second part of the talk I will show that the Unique Games Conjecture is false when the underlying constraint graph is a (spectral) expander. Namely, I will present a polynomial-time algorithm for Unique Games on expanding instances that finds a good assignment when there exists one. ©2009 Microsoft Corporation. All rights reserved.

In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs.

In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs.

Journal of Optimization Theory and Applications 1991: Volume 69 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1991-03_68_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1991-04_69_1 .

Journal of Optimization Theory and Applications 1993: Volume 79 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1993-09_78_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1993-10_79_1 .

Journal of Optimization Theory and Applications 1995: Volume 85 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1995-03_84_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1995-04_85_1 .

Journal of Optimization Theory and Applications 1996: Volume 90 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-06_89_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-07_90_1 .

Journal of Optimization Theory and Applications 1998: Volume 96 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1996-12_91_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1998-01_96_1 .

Journal of Optimization Theory and Applications 1967: Volume 1 , Issue Index. Digitized from IA1534532-04 . Next issue: sim_journal-of-optimization-theory-and-applications_1967-07_1_1 .

Journal of Optimization Theory and Applications 1995: Volume 84 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1994-12_83_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1995-01_84_1 .

General nonconvex optimization problems are studied by using the canonical duality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema. Detailed applications are illustrated by several examples.

Graduate research activity in the following areas is reported: the divergence of laminated composite lifting surfaces, subsonic propeller theory and aeroelastic analysis, and cross sectional resonances in wind tunnels.

A queues through investigations of probability distributions generated and directed to the flow of customers and services to meet the demand of new customers waiting time in queues through practical ways. This work had as objective, a real reduction in the service queue of an ice cream shop. They were selected according to the specific needs of the optimization of processes, eliminating bottlenecks and processes. Some services have taken into account the peculiarities of the place, and public, having been receiving quality services and financially for the clients.

A queues through investigations of probability distributions generated and directed to the flow of customers and services to meet the demand of new customers waiting time in queues through practical ways. This work had as objective, a real reduction in the service queue of an ice cream shop. They were selected according to the specific needs of the optimization of processes, eliminating bottlenecks and processes. Some services have taken into account the peculiarities of the place, and public, having been receiving quality services and financially for the clients.

Purpose:  This study aimed to optimize the stock portfolio based on stochastic matrix theory in the stock market and to answer whether the relevant information will exist using the Marčenko–Pastur distribution. Methodology:  The data of 31 shares in the Tehran Stock Exchange in 2016 - 2019 will be examined for cross-correlation between shares. So, there will be 749 end-of-day prices and 748 logarithms of returns. This research was done using the descriptive-correlation method and is of an applied research type. Findings:  The results showed: a) Observing the most extensive distribution of eigenvector components, it can be seen that there is a solid asymmetry to the left of the distribution, meaning that the market responds more to bad events than good events. b) By clearing the correlation matrix, the difference between the predicted and realized risk can be slightly reduced. In other words, the risk is reduced by identifying and removing non-valuable stocks from the portfolio portfolio. c) A stochastic stock matrix can significantly predict the realized return and risk of the market and, therefore, explain the risk of market information. d) The inverse participation ratio determines the stocks affecting the particular vectors, and the primary analysis of random matrices is based on adjusting this ratio using random matrix clearance. Originality/Value:  Unlike other portfolio formation methods determining the weight of each asset in the portfolio,   stochastic matrix theory identifies unused stocks and removes them from the stock portfolio, thereby improving portfolio return and risk.

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.

Journal of Optimization Theory and Applications 1978: Volume 25 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978-04_24_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1978_25_contents .

Journal of Optimization Theory and Applications 1979: Volume 27 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1979_27_index . Next issue: sim_journal-of-optimization-theory-and-applications_1979-01_27_1 .

Journal of Optimization Theory and Applications 1982: Volume 37 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1982-04_36_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1982-05_37_1 .

Journal of Optimization Theory and Applications 1992: Volume 74 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1992-06_73_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1992-07_74_1 .

A working theory of two-component two-phase (gas-liquid) nozzles, developed as part of Phase I, was used to conduct parametric performance analyses over a wide range of flow conditions and for varied fluid properties. Droplet breakup and the interface transport of momentum and thermal energy were considered in the analyses, but mass transfer and wall friction losses were excluded. Results from the parametric analyses compare favorably with experimental data and other theoretical analyses available in the literature. The sensitivity of the predicted nozzle performance to the assumptions concerning the droplet characteristics was examined, and criteria were developed for optimum nozzle designs based on the parametric analyses. A simplified procedure was developed for the quick estimation of the major dimensions for two-phase nozzles. Finally, the work extraction potential of two-phase nozzles was examined in terms of their performance criteria and system integration characteristics.

The research described in this report deals with the development of (1) efficient, consistent discretization techniques for use in semi-infinite optimization, optimal control algorithms that solve problems with dynamics governed by partial differential equations, (2) superlinearly converging semi- finite optimization algorithms, (3) various techniques for finding design parameters satisfying specifications, (4) optimal control algorithms for discrete and distributed systems with control, state and shape constraints, and (5) efficient numerical procedures for the integrated design of flexible structures and their control systems.... Optimization, Optimal shape design algorithms.

In the Internet today, traffic management spans congestion control (at end hosts), routing protocols (on routers), and traffic engineering (by network operators). Historically, this division of functionality evolved organically. This talk presents a top-down redesign of traffic management using recent innovations in optimization theory. First, we propose an objective function that captures the goals of end users and network operators. Using all known optimization decomposition techniques, we generate four distributed algorithms that divide traffic over multiple paths based on feedback from the network links. Combining the best features of the algorithms, we construct a traffic management protocol that is distributed, adaptive, robust, flexible and easy to manage. Further, our new protocol can operate based on implicit feedback about packet loss and delay. We show that using optimization decompositions as a foundation, simulations as a building block, and human intuition as a guide can be a principled approach to protocol design. This is joint work with Jiayue He, Martin Suchara, Ma’ayan Bresler, and Mung Chiang. ©2009 Microsoft Corporation. All rights reserved.

This paper considers optimization over multiple renewal systems coupled by time average constraints. These systems act asynchronously over variable length frames. For each system, at the beginning of each renewal frame, it chooses an action which affects the duration of its own frame, the penalty, and the resource expenditure throughout the frame. The goal is to minimize the overall time average penalty subject to several overall time average resource constraints which couple these systems. This problem has applications to task processing networks, coupled Markov decision processes(MDPs) and so on. We propose a distributed algorithm so that each system can make its own decision after observing a global multiplier which is updated slot-wise. We show that this algorithm satisfies the desired constraints and achieves $\mathcal{O}(\varepsilon)$ near optimality with $\mathcal{O}(1/\varepsilon^2)$ convergence time.

Journal of Optimization Theory and Applications 1980: Volume 31 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1980-04_30_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1980-05_31_1 .

Journal of Optimization Theory and Applications 1996: Volume 88 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1995-12_87_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1996-01_88_1 .

The traditional stochastic resonance is realized by adding an optimal amount of noise, while the parameter tuning stochastic resonance is realized by optimally tuning the system parameters. The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints on system parameters and noise intensity, which is proven to have one and only one local maximum for the Gaussian-distributed weak input signal.

The traditional stochastic resonance is realized by adding an optimal amount of noise, while the parameter tuning stochastic resonance is realized by optimally tuning the system parameters. The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints on system parameters and noise intensity, which is proven to have one and only one local maximum for the Gaussian-distributed weak input signal.

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In the Internet today, traffic management spans congestion control (at end hosts), routing protocols (on routers), and traffic engineering (by network operators). Historically, this division of functionality evolved organically. This talk presents a top-down redesign of traffic management using recent innovations in optimization theory. First, we propose an objective function that captures the goals of end users and network operators. Using all known optimization decomposition techniques, we generate four distributed algorithms that divide traffic over multiple paths based on feedback from the network links. Combining the best features of the algorithms, we construct a traffic management protocol that is distributed, adaptive, robust, flexible and easy to manage. Further, our new protocol can operate based on implicit feedback about packet loss and delay. We show that using optimization decompositions as a foundation, simulations as a building block, and human intuition as a guide can be a principled approach to protocol design. This is joint work with Jiayue He, Martin Suchara, Ma’ayan Bresler, and Mung Chiang. ©2009 Microsoft Corporation. All rights reserved.

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Journal of Optimization Theory and Applications 2002: Volume 115 , Issue Contents. Digitized from IA1534532-02 . Previous issue: sim_journal-of-optimization-theory-and-applications_2002-09_114_3 . Next issue: sim_journal-of-optimization-theory-and-applications_2002-10_115_1 .

Journal of Optimization Theory and Applications 1975: Volume 15 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1974-12_14_6 . Next issue: sim_journal-of-optimization-theory-and-applications_1975-01_15_1 .

Journal of Optimization Theory and Applications 1978: Volume 25 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978_25_index . Next issue: sim_journal-of-optimization-theory-and-applications_1978-05_25_1 .

Journal of Optimization Theory and Applications 1979: Volume 27 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1978-12_26_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1979_27_contents .

Journal of Optimization Theory and Applications 1980: Volume 30 , Issue Index. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1980_30_contents . Next issue: sim_journal-of-optimization-theory-and-applications_1980-01_30_1 .

The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a practitioner point of view is rightful to wander "which optimization method is the best for my problem?". Looking at the optimization process as a "system" of intercon- nected parts, in this paper are collected some ideas about how to tackle an optimization problem using a class of tools from evolutionary computations called Genetic Algorithms. Despite the number of optimization techniques available nowadays the author of this paper thinks that Genetic Algorithms still play a central role for their versatility, robustness, theoretical framework and simplicity of use. The paper can be considered a "collection of tips" (from literature and personal experience) for the non-computer-scientist that has to deal with optimization problems both in the science and engineering practice. No original methods or algorithms are proposed.

The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a practitioner point of view is rightful to wander "which optimization method is the best for my problem?". Looking at the optimization process as a "system" of intercon- nected parts, in this paper are collected some ideas about how to tackle an optimization problem using a class of tools from evolutionary computations called Genetic Algorithms. Despite the number of optimization techniques available nowadays the author of this paper thinks that Genetic Algorithms still play a central role for their versatility, robustness, theoretical framework and simplicity of use. The paper can be considered a "collection of tips" (from literature and personal experience) for the non-computer-scientist that has to deal with optimization problems both in the science and engineering practice. No original methods or algorithms are proposed.

This study discusses the factors related to the optimal selection of aimpoints for direct fire. Mean point of impact or bias errors and round-to- round or precision errors are considered. The concepts and techniques related to the problem are developed through a series of examples. A study looking into the effects of varying the precision errors is presented. Keywords: Target location density; Precision errors; Aimpoint strategy; Circular error probable; Gunnery.

The motivating application for this research is the global/local optimal design of composite aircraft structures such as wings and fuselages, but the theory and algorithms are more widely applicable in engineering design. Research is proposed on three distinct topics. (1) Rigorous mathematical theory will be developed supporting a decomposition strategy for global/local optimization. Advanced computational and numerical approximation techniques, such as massively parallel computing and surrogate functions, will be used in the decomposition. (2) Local panel optimization algorithms that can handle both discrete and continuous variables efficiently will be investigated. Several different strategies for blending local composite panel designs to improve manufacture will be developed and tested. (3) Mathematical theory and parallel computing paradigms for cellular automata applied to structural design will be developed and validated on a variety of structural design problems. Comparison to standard FEM-based optimization will be done.

Contents: Differential Calculus in Normed Linear Spaces; Minimisation of Functionals; Minimisation Without Constraints; Minimization with Constraints; Duality and Its Applications; Elements of the Theory of Control. Lecture Notes Collection FreeScience.info ID2729 Obtained from http://www.math.tifr.res.in/~publ/ln/tifr53.pdf http://www.freescience.info/go.php?pagename=books&id=2729

Development and application of optimization techniques to water pollution, social choice, and game theory. (Author)

Journal of Optimization Theory and Applications 1989: Volume 63 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1989-09_62_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1989-10_63_1 .

Journal of Optimization Theory and Applications 1991: Volume 71 , Issue Contents. Digitized from IA1534532-03 . Previous issue: sim_journal-of-optimization-theory-and-applications_1991-09_70_3 . Next issue: sim_journal-of-optimization-theory-and-applications_1991-10_71_1 .

Journal of Optimization Theory and Applications 1985: Volume 47 , Issue Contents. Digitized from IA1534532-04 . Previous issue: sim_journal-of-optimization-theory-and-applications_1985-08_46_4 . Next issue: sim_journal-of-optimization-theory-and-applications_1985-09_47_1 .

Bell System Technical Journal, 45: 5. May-June 1966 pp 761-764. B.S.T.J. Briefs: A Note on a Type of Optimization Problem that Arisesin Communication Theory. (Sandberg, I.W.)