Downloads & Free Reading Options - Results

A mobile manipulator generally possesses kinematic redundancy, which requires some method for selecting the configuration appropriate to the task. Evolutionary Programming (EP) has been used successfully to select an appropriate configuration using a large penalty on the end-point position to force the end-point to the goal position for the task. This paper demonstrates that using an equality constraint for the end-point position results in much faster convergence to approximately the same final configurations. The reasons for this increase in speed are examined using a simplified model to determine the relative size of their effects.

Binary optimization is one of the central problems in mathematical optimization and it captures an abundance of applications. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose two penalization/regularization methods (exact penalty and alternating direction) to solve it. The resulting algorithms seek desirable solutions to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that both the penalty function and augmented Lagrangian function, induced by adding the complementarity constraint to the objectives, are exact, i.e., they have the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of both algorithms can be guaranteed since they essentially reduce to block coordinate descent in the literature. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including graph bisection, constrained image segmentation, dense subgraph discovery, modularity clustering and Markov random fields. Extensive experiments show that our methods outperform existing popular techniques, such as iterative hard thresholding, linear programming relaxation and semidefinite programming relaxation.

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state of the art abductive systems and answer set solvers and showing how to use it to program some applications. (To appear in Theory and Practice of Logic Programming - TPLP).

Many large-scale optimization problems can be formulated as nonlinear programming problems where the constraints represent systems governed by partial differential equations. This deceptively simple observation allows for a wealth of possibilities in the development of optimization methods applicable to such problems. This is a vast area of research on problems of importance to the nations environment, economy, and defense. The work reported here had as its goal the development and evaluation of a number of different optimization strategies for problems with simulation constraints. Specifically, the work focused on applying direct search methods to and developing interior-point algorithms for problems of this form.

This paper studies the linear optimization problem subject to a system of bipolar fuzzy relation equations with the max-product composition operator. Its feasible domain is briefly characterized by its lower and upper bound, and its consistency is considered. Also, some sufficient conditions are proposed to reduce the size of the search domain of the optimal solution to the problem. Under these conditions, some equations can be deleted to compute the minimum objective value. Some sufficient conditions are then proposed which under them, one of the optimal solutions of the problem is explicitly determined and the uniqueness conditions of the optimal solution are expressed. Moreover, a modified branch-and-bound method based on a value matrix is proposed to solve the reduced problem. A new algorithm is finally designed to solve the problem based on the conditions and modified branch-and-bound method. The algorithm is compared to the methods in other papers to show its efficiency.

Theil and van de Panne have shown how to replace the problem of maximizing a (strictly concave) quadratic function subject to linear inequality constraints by a finite sequence of sub-problems involving only linear equality constraints. In another paper, the author generalized this approach to (i) cover the case of a differentiable and strictly concave objective function, and (ii) permit almost complete flexibility in the choice of the initial sub- problem. The last feature seems essential for the approach to be of computational interest, for computational experience suggests that the number of sub-problems that must be solved and the amount of computer storage required to keep track of them have a tendency to grow approximately exponentially with the 'poorness' of the choice of the initial sub-problem. In this paper a modification of the above approach is proposed which generates the sub-problems in Markovian fashion. This all but eliminates the storage problem. Although the resulting sequence of sub-problems is no longer necessarily finite, by means of the theory of Markov chains it is shown that eventual convergence to the optimum is assured with probability one and argued that the expected number of sub-problems that must be solved increases only approximately linearly with the 'poorness' of the initial sub-problem. Computational evidence is given which supports this estimate and suggests the probable efficiency of the Markovian algorithm even for quite 'bad' choices of the initial sub-problem.

The purpose of the paper is to illustrate how the functional equation technique of the theory of dynamic programming may be employed to treat a class of variational problems with constraints.

Dataflow languages provide natural support for specifying constraints between objects in dynamic applications, where programs need to react efficiently to changes of their environment. Researchers have long investigated how to take advantage of dataflow constraints by embedding them into procedural languages. Previous mixed imperative/dataflow systems, however, require syntactic extensions or libraries of ad hoc data types for binding the imperative program to the dataflow solver. In this paper we propose a novel approach that smoothly combines the two paradigms without placing undue burden on the programmer. In our framework, programmers can define ordinary commands of the host imperative language that enforce constraints between objects stored in "reactive" memory locations. Reactive objects can be of any legal type in the host language, including primitive data types, pointers, arrays, and structures. Constraints are automatically re-executed every time their input memory locations change, letting a program behave like a spreadsheet where the values of some variables depend upon the values of other variables. The constraint solving mechanism is handled transparently by altering the semantics of elementary operations of the host language for reading and modifying objects. We provide a formal semantics and describe a concrete embodiment of our technique into C/C++, showing how to implement it efficiently in conventional platforms using off-the-shelf compilers. We discuss relevant applications to reactive scenarios, including incremental computation, observer design pattern, and data structure repair. The performance of our implementation is compared to ad hoc problem-specific change propagation algorithms and to language-centric approaches such as self-adjusting computation and subject/observer communication mechanisms, showing that the proposed approach is efficient in practice.

Dataflow languages provide natural support for specifying constraints between objects in dynamic applications, where programs need to react efficiently to changes of their environment. Researchers have long investigated how to take advantage of dataflow constraints by embedding them into procedural languages. Previous mixed imperative/dataflow systems, however, require syntactic extensions or libraries of ad hoc data types for binding the imperative program to the dataflow solver. In this paper we propose a novel approach that smoothly combines the two paradigms without placing undue burden on the programmer. In our framework, programmers can define ordinary commands of the host imperative language that enforce constraints between objects stored in "reactive" memory locations. Reactive objects can be of any legal type in the host language, including primitive data types, pointers, arrays, and structures. Constraints are automatically re-executed every time their input memory locations change, letting a program behave like a spreadsheet where the values of some variables depend upon the values of other variables. The constraint solving mechanism is handled transparently by altering the semantics of elementary operations of the host language for reading and modifying objects. We provide a formal semantics and describe a concrete embodiment of our technique into C/C++, showing how to implement it efficiently in conventional platforms using off-the-shelf compilers. We discuss relevant applications to reactive scenarios, including incremental computation, observer design pattern, and data structure repair. The performance of our implementation is compared to ad hoc problem-specific change propagation algorithms and to language-centric approaches such as self-adjusting computation and subject/observer communication mechanisms, showing that the proposed approach is efficient in practice.

In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ including each of constraint string in $P$ as a substring and the length of $Z$ is maximized. A new dynamic programming solution to this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(d2^dnmr)$. In the case of the number of constraint strings is fixed, our new algorithm for the generalized longest common subsequence problem with multiple substring inclusive constraints requires $O(nmr)$ time and space.

What is the value of information in solving linear programming? The celebrated ellipsoid algorithm tells us that the full information of input constraints is not necessary; the algorithm works as long as there exists an oracle that, on a proposed candidate solution, returns a violation in the format of a separating hyperplane. Can linear programming still be efficiently solved if the returned violation is in another format? We study this question in a trial-and-error setting: there is an oracle that, upon a proposed solution, returns the index of an arbitrary violated constraint (with the content of the constraint still hidden). We give an algorithm with running time O(m^{poly(n)} L), where m and n are the numbers of constraints and variables, respectively, and L is the input size of the linear program. The exponential dependence on n is unfortunately unavoidable; we show a lower bound of \Omega(m^{\lfloor n/2\rfloor}) on the number of queries needed. Meanwhile, if the oracle provides more violation information---the index of a "most violated" constraint, measured by the Euclidean distance of the proposed solution and the half-spaces defined by the constraints---then we show that the linear program can be solved in polynomial time. The proofs of the results employ a variety of geometric techniques, including McMullen's Upper Bound Theorem, the weighted spherical Voronoi diagram, and the furthest Voronoi diagram. In addition, we give an alternative proof to a conjecture of L\'aszl\'o Fejes T\'oth on bounding the number of disconnected components formed by the union of m convex bodies in R^n. Our proof, inspired by the Gauss-Bonnet Theorem in global differential geometry, is independent of the known and clearly reveals more insights into the problem and bound.

We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean (i.e. restricted to $\{0,1\}$), the maximum solution problem is identical to the well-studied \prob{Max Ones} problem, and the approximability is completely understood for all restrictions on the underlying constraints [Khanna et al., SIAM J. Comput., 30 (2001), pp. 1863-1920]. We continue this line of research by considering domains containing more than two elements. We present two main results: a complete classification for the approximability of all maximal constraint languages over domains of cardinality at most 4, and a complete classification of the approximability of the problem when the set of allowed constraints contains all permutation constraints. Under the assumption that a conjecture due to Szczepara holds, we give a complete classification for all maximal constraint languages. These classes of languages are well-studied in universal algebra and computer science; they have, for instance, been considered in connection with machine learning and constraint satisfaction. Our results are proved by using algebraic results from clone theory and the results indicates that this approach is very powerful for classifying the approximability of certain optimisation problems.

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to handle inconsistent linearizations. Numerical tests are performed to investigate the behaviour of the class of algorithms.

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on Iterative Hard Thresholding (IHT). In this paper, we consider a class of continuous optimization techniques based on Mathematical Programs with Equilibrium Constraints (MPECs) to solve general sparsity constrained problems. Specifically, we reformulate the problem as an equivalent biconvex MPEC, which we can solve using an exact penalty method or an alternating direction method. We elaborate on the merits of both proposed methods and analyze their convergence properties. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including feature selection, segmented regression, MRF optimization, trend filtering and impulse noise removal. Extensive experiments show that our MPEC-based methods outperform state-of-the-art techniques, especially those based on IHT.

We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time $2^{(1-\text{poly}(1/c))n}$ where n is the number of variables and cn is the number of constraints. The key idea for the algorithm is a reduction to the Vector Domination problem and a new algorithm for that subproblem.

The objective of this paper is to design an efficient and convergent alternating direction method of multipliers (ADMM) for finding a solution of medium accuracy to conic programming problems whose constraints consist of linear equalities, linear inequalities, a non-polyhedral cone and a polyhedral cone. For this class of problems, one may apply the directly extended ADMM to their dual, which can be written in the form of convex programming with four separable blocks in the objective function and a coupling linear equation constraint. Indeed, the directly extended ADMM, though may diverge in theory, often performs much better numerically than many of its variants with theoretical convergence guarantee. Ideally, one should find a convergent variant which is at least as efficient as the directly extended ADMM in practice. We achieve this goal by designing a convergent semi-proximal ADMM (called sPADMM3c for convenience) for convex programming problems having three separable blocks in the objective function with the third part being linear. At each iteration, the proposed sPADMM3c takes one special block coordinate descent (BCD) cycle with the order $1 \rightarrow 3 \rightarrow 2 \rightarrow 3$, instead of the usual $1 \rightarrow 2 \rightarrow 3$ Gauss-Seidel BCD cycle used in the non-convergent directly extended $3$-block ADMM, for updating the variable blocks. Our extensive numerical tests on the important class of doubly non-negative semidefinite programming (SDP) problems with linear equality and/or inequality constraints demonstrate that our convergent method is at least $20%$ faster than the directly extended ADMM with unit step-length for the vast majority of about $550$ large scale problems tested.

This research investigated an alternative to the traditional approaches of optimizing a stochastic response surface subject to constraints. This research investigated the bias in the expected value of the solution, possible alternative decision variable settings, and a method to improve the solution. A three step process is presented to evaluate stochastic response surfaces subject to constraints. Step 1 is to use a traditional approach to estimate the response surface and a covariance matrix through regression. Step 2 samples the objective function of the linear program (i.e., response surface) and identifies the extreme points visited. Step 3 presents a method to estimate the optimal extreme point and present that information to a decision maker.

Monomials function has always been considered as a significant and most extensively used function in real living. Resource allocation, structure optimization and technology management can often apply these functions. In optimization problems the objective functions can be considered by monomials. In this paper, we present monomials geometric programming with fuzzy relation inequalities constraint with max-product composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and a few practical examples are presented to abbreviate and illustrate the steps of the problem resolution.

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

This dissertation involves the solution of a convex nonlinear programming problem using a primal-dual algorithm developed in McCormick(1991a and 1991b)

We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the complementarity measure and a nonlinear programming with general constraints. A strategy generalizing ideas of Byrd-Omojokun's trust region method is used to compute steps. By penalizing the tangential constraints into the objective function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like strategy is used to balance the improvements on feasibility and optimality. We show that, under MPEC-MFCQ, if the algorithm does not terminate in finite steps, then at least one accumulation point of the iterates sequence is an S-stationary point.

We give a quick and dirty, but reasonably safe, algorithm for the minimization of a convex quadratic function under convex quadratic constraints. The algorithm minimizes the Lagrangian dual by using a safeguarded Newton method with non-negativity constraints.

This volume was digitized and made accessible online due to deterioration of the original print copy.

A finitely convergent procedure is given for maximizing a differentiable and strictly concave function subject to linear constraints. It is also assumed that the objective function attains its unconstrained maximum. No additional assumptions whatever are required. The procedure is aimed directly at constructing a solution of a certain version of the Kuhn-Tucker Conditions. Provision is made for utilizing a priori information regarding which constraints are likely to be satisfied exactly at the optimum. When applied to quadratic programming, the procedure specializes to a promising generalization of Theil and van de Panne's algorithm.

This describes a C version of a infeasible primal-dual algorithm for positive definite quadratic programming with box constraints, proposed by Voglis and Lagaris. We also give a straightforward .C() interface for R.

Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics. Propositional logic is, arguably, the simplest ASP system with an intuitive semantics supporting direct modeling of problem constraints. However, for some applications, especially those requiring that transitive closure be computed, it requires additional variables and results in large theories. Consequently, it may not be a practical computational tool for such problems. On the other hand, ASP systems based on nonmonotonic logics, such as stable logic programming, can handle transitive closure computation efficiently and, in general, yield very concise theories as problem representations. Their semantics is, however, more complex. Searching for the middle ground, in this paper we introduce a new nonmonotonic logic, DATALOG with constraints or DC. Informally, DC theories consist of propositional clauses (constraints) and of Horn rules. The semantics is a simple and natural extension of the semantics of the propositional logic. However, thanks to the presence of Horn rules in the system, modeling of transitive closure becomes straightforward. We describe the syntax and semantics of DC, and study its properties. We discuss an implementation of DC and present results of experimental study of the effectiveness of DC, comparing it with CSAT, a satisfiability checker and SMODELS implementation of stable logic programming. Our results show that DC is competitive with the other two approaches, in case of many search problems, often yielding much more efficient solutions.

MINOS is a Fortran program designed to minimize a linear or nonlinear function subject to linear constraints, where the constraint matrix is in general assumed to be large and sparse. The User's Guide contains an overview of the MINOS System, including descriptions of the theoretical algorithms as well as the details of implementation. The Guide also provides complete instructions for the use of MINOS, and illustrates the diversity of application by several examples. (Author)

The report is concerned with methods of approximating the chance- constrained set S = (x such that/Pr(A x=or B)=or alpha) when the underlying distribution, F(.) of the random variate (A, B) is non-normal. The resulting sets are completely distribution-free in that no assumptions are made about the form of F(.) or any of its parameters. The concept employed is the distribution- free tolerance region. This is a sample based region containing 100 alpha percent of the population, at a confidence level, beta. The elements of the distribution-free sets satisfy the chance-constraint, Pr(Ax = or B) =or alpha with a confidence of at least beta. Furthermore, the sample size required to attain this level of confidence is readily available in tabular or graphical form. The superiority of the distribution-free approach over existing chance- constrained methods is demonstrated using simulated gamma variates.

Monomials function has always been considered as a significant and most extensively used function in real living. Resource allocation, structure optimization and technology management can often apply these functions. In optimization problems the objective functions can be considered by monomials. In this paper, we present monomials geometric programming with fuzzy relation inequalities constraint with max-product composition.

In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the associated random outcome vector of interest is preferable to a specified benchmark with respect to the multivariate polyhedral conditional value-at-risk (CVaR) or a multivariate stochastic order relation. In this case, the classical decomposition methods cannot be used directly due to the complicating multivariate stochastic benchmarking constraints. We propose an exact unified decomposition framework for solving these two classes of optimization problems and show its finite convergence. We apply the proposed approach to a stochastic network design problem in a pre-disaster humanitarian logistics context and conduct a computational study concerning the threat of hurricanes in the Southeastern part of the United States. Our numerical results on these large-scale problems show that our proposed algorithm is computationally scalable.

In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL$+$, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL$+$ is a much enhanced version of SDPNAL introduced by Zhao, Sun and Toh [SIAM Journal on Optimization, 20 (2010), pp.~1737--1765] for solving generic SDPs. SDPNAL works very efficiently for nondegenerate SDPs but may encounter numerical difficulty for degenerate ones. Here we tackle this numerical difficulty by employing a majorized semismooth Newton-CG augmented Lagrangian method coupled with a convergent 3-block alternating direction method of multipliers introduced recently by Sun, Toh and Yang [arXiv preprint arXiv:1404.5378, (2014)]. Numerical results for various large scale SDPs with or without nonnegative constraints show that the proposed method is not only fast but also robust in obtaining accurate solutions. It outperforms, by a significant margin, two other competitive publicly available first order methods based codes: (1) an alternating direction method of multipliers based solver called SDPAD by Wen, Goldfarb and Yin [Mathematical Programming Computation, 2 (2010), pp.~203--230] and (2) a two-easy-block-decomposition hybrid proximal extragradient method called 2EBD-HPE by Monteiro, Ortiz and Svaiter [Mathematical Programming Computation, (2013), pp.~1--48]. In contrast to these two codes, we are able to solve all the 95 difficult SDP problems arising from the relaxations of quadratic assignment problems tested in SDPNAL to an accuracy of $10^{-6}$ efficiently, while SDPAD and 2EBD-HPE successfully solve 30 and 16 problems, respectively.

The optimal timing of air-to-ground tasks is undertaken. Specifically, a scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. The vehicles must perform multiple tasks on each target. The targets must be found, classified, attacked, and verified as destroyed. The optimal performance of these tasks requires cooperation amongst the vehicles such that critical timing constraints are satisfied. In this paper, an optimal task assignment and timing algorithm is developed, using a mixed integer linear program, or MILP, formulation. MILP can be used to assign all tasks to the vehicles in an optimal manner, including variable arrival times, for groups of air vehicles with coupled tasks involving timing and task order constraints. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.

Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints - like checking the consistency of a program - are intractable. Many intractable problems in the area of knowledge representation and reasoning have been shown to become linear time tractable if the treewidth of the programs or formulas under consideration is bounded by some constant. The goal of this paper is to apply the notion of treewidth to programs with cardinality or weight constraints and to identify tractable fragments. It will turn out that the straightforward application of treewidth to such class of programs does not suffice to obtain tractability. However, by imposing further restrictions, tractability can be achieved.

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.

http://uf.catalog.fcla.edu/uf.jsp?st=UF026891698&ix=pm&I=0&V=D&pm=1

Document discusses a new algorithm for the separable convex programming with linear constraints. This is based on the approximation of the objective function by at most two linear pieces in the neighborhood of the current feasible solution. The two segments will be adaptively defined rather than predecided fixed grids. If, furthermore, the objective function is differentiable, and one introduces a non-Archimedean infinitesimal, the algorithm generates a sequence of feasible solutions every cluster point of which is an optimal solution. Computational tests on the problem with up to 196 non-linear variables is presented. (Author)