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This article provides instructions in preparing a paper for publication in the "Journal of Optimization Theory and Applications." Some of these guidelines are the following: 1)submission of manuscripts in triplicate; 2) reference to English as the official language of the journal; 3) inclusion of an abstract of at least 50 to 100 words in each contribution; and, 4) the abstract should be followed by a list of four to five key words identifying the subject.

Rufus P. Isaacs joined the RAND Corporation4. Santa Monica, California in 1948 and started to develop the theory of dynamic games in the early 1950s. Until winter 1954/55, when Isaacs left the RAND Corporation, he investigated two player. zero-sum dynamic games of the classic pursuit-evasion type. Prior to 1965, Isaacs published his theory only in internal RAND papers and research memoranda. In his first RAND paper (Ref. 1), Isaacs sketched the basic ideas of zero-sum dynamic game theory The ideas already included rudimentary precursors of the maximum principle, dynamic programming, and backward analysis. At the end of 1954 and the beginning of 1955. Isaacs summarized his research in four research memoranda (Refs. 3–6), which ten years later formed the basis of his famous book on Differential Games (Ref. 7). This paper survey's Isaacs' research with an emphasis on the early years of dynamic games. The readers are kindly invited to discuss the author's point of view. Comments and statements sent to the author will be summarized and published later. [ABSTRACT FROM AUTHOR]

This paper studies the tracking and almost disturbance decoupling problem of the nonlinear AMIRA ball and beam system based on the feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. Two examples on the almost disturbance decoupling problem, which cannot be solved via Ref. 1, are proposed in this paper exploiting the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a new sequential penalty algorithm, based on the L[sub ∞] exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. [ABSTRACT FROM AUTHOR]

This article provides the editorial policy of the "Journal of Optimization Theory and Applications." The journal publishes carefully selected papers covering mathematical optimization techniques and their applications to science and engineering. And it issues five types of contributions such as Survey Papers, Contributed Papers, and Technical Notes. Manuscripts, in triplicate, may be submitted to any of the Associate Editors or the Editor-in-Chief.

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied. [ABSTRACT FROM AUTHOR]

This paper deals with a parametric family of convex semi-infinite optimization problems for which linear perturbations of the objective function and continuous perturbations of the right-hand side of the constraint system are allowed. In this context, Cánovas et al. (SIAM J. Optim. 18:717–732, []) introduced a sufficient condition (called ENC in the present paper) for the strong Lipschitz stability of the optimal set mapping. Now, we show that ENC also entails high stability for the minimal subsets of indices involved in the KKT conditions, yielding a nice behavior not only for the optimal set mapping, but also for its inverse. Roughly speaking, points near optimal solutions are optimal for proximal parameters. In particular, this fact leads us to a remarkable simplification of a certain expression for the (metric) regularity modulus given in Cánovas et al. (J. Glob. Optim. 41:1–13, []) (and based on Ioffe (Usp. Mat. Nauk 55(3):103–162, []; Control Cybern. 32:543–554, [])), which provides a key step in further research oriented to find more computable expressions of this regularity modulus. [ABSTRACT FROM AUTHOR]

This paper proposes several globally convergent geometric optimization algorithms on Riemannian manifolds, which extend some existing geometric optimization techniques. Since any set of smooth constraints in the Euclidean space Rn (corresponding to constrained optimization) and the Rn space itself (corresponding to unconstrained optimization) are both special Riemannian manifolds, and since these algorithms are developed on general Riemannian manifolds, the techniques discussed in this paper provide a uniform framework for constrained and unconstrained optimization problems. Unlike some earlier works, the new algorithms have less restrictions in both convergence results and in practice. For example, global minimization in the one-dimensional search is not required. All the algorithms addressed in this paper are globally convergent. For some special Riemannian manifold other than Rn, the newalgorithms are very efficient. Convergence rates are obtained. Applications are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a surrogate constraint tabu thresholding (SCTT) implementation for solving the frequency assignment problem. The frequency assignment problem is an important combinatorial optimisation problem that arises in telecommunications. The main objective is to assign radio frequencies to a number of communication links such that interference is minimised. Interference is minimised by satisfying a number of problem specific constraints. The surrogate constraint is created by taking a weighted sum of the constraints not satisfied. SCTT is compared with a tabu thresholding method from the literature on a set of simulated but realistic test problems with respect to quality of the solution in a given time period. Computational results show that SCTT is more efficient and effective for all the test problems. [ABSTRACT FROM AUTHOR]

This paper explores the use of simulated annealing (SA) for solving arbitrary combinatorial optimisation problems. It reviews an existing code called GPSIMAN for solving 0–1 problems, and evaluates it against a commercial branch-and-bound code, OSL. The problems tested include travelling salesman, graph colouring, bin packing, quadratic assignment and generalised assignment. The paper then describes a technique for representing these problems using arbitrary integer variables, and shows how a general simulated annealing algorithm can also be applied. This new code, INTSA, outperforms GPSIMAN and OSL on almost all of the problems tested. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush-Kuhn-Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established. [ABSTRACT FROM AUTHOR]

A chance constrained optimization problem over a finite distribution involves a set of scenario constraints from which a small subset can be violated. We consider the setting where all scenario constraints are mixed-integer convex. Existing works typically consider a mixed integer nonlinear programming (MINLP) formulation of this problem by introducing binary variables to indicate which constraint systems are to be satisfied or violated. A variety of cutting plane approaches for this MINLP formulation have been developed. In this paper we consider a family of cuts in the original space rather than those in the extended space of the MINLP reformulation. These cuts, known as quantile cuts, can be viewed as a projection of the well known family of mixing inequalities for the MINLP reformulation onto the original problem space. We show that the closure of the infinite family of all quantile cuts has a finite description. An important corollary of this result is that for linear chance constrained problems the quantile closure is polyhedral. We further show that a recursive application of quantile closure operations recovers the convex hull of the nonconvex chance constrained set in the limit, and in the pure integer setting the convergence is finite. We show that separation of quantile cuts is in general NP-hard, develop a heuristic separation method, and demonstrate its effectiveness through a computational study. We also study an approximation of the quantile closure and propose a generalization by grouping scenarios. [ABSTRACT FROM AUTHOR]

The zero propellant maneuver (ZPM) is an advanced space station, large angle attitude maneuver technique, using only control momentum gyroscopes (CMGs). Path planning is the key to success, and this paper studies the associated multi-objective optimization problem. Three types of maneuver optimal control problem are formulated: (i) momentum-optimal, (ii) time-optimal, and (iii) energy-optimal. A sensitivity analysis approach is used to study the Pareto optimal front and allows the tradeoffs between the performance indices to be investigated. For example, it is proved that the minimum peak momentum decreases as the maneuver time increases, and the minimum maneuver energy decreases if a larger momentum is available from the CMGs. The analysis is verified and complemented by the numerical computations. Among the three types of ZPM paths, the momentum-optimal solution and the time-optimal solution generally possess the same structure, and they are singular. The energy-optimal solution saves significant energy, while generally maintaining a smooth control profile. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. [ABSTRACT FROM AUTHOR]

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi (Math. Program. 39(2):117-129, ) that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix is in the copositive cone, is a co-NP-complete problem. From this it has long been assumed that this implies that the question of whether or not the strong membership problem for the dual of the copositive cone, the completely positive cone, is also an NP-hard problem. However, the technical details for this have not previously been looked at to confirm that this is true. In this paper it is proven that the strong membership problem for the completely positive cone is indeed NP-hard. Furthermore, it is shown that even the weak membership problems for both of these cones are NP-hard. We also present an alternative proof of the NP-hardness of the strong membership problem for the copositive cone. [ABSTRACT FROM AUTHOR]

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a decentralized parallel computation model for global optimization using interval analysis. The model is adaptive to any number of processors and the workload is automatically and evenly distributed among all processors by alternative message passing. The problems received by each processor are processed based on their local dominance properties, which avoids unnecessary interval evaluations. Further, the problem is treated as a whole at the beginning of computation so that no initial decomposition scheme is required. Numerical experiments indicate that the model works well and is stable with different number of parallel processors, distributes the load evenly among the processors, and provides an impressive speedup, especially when the problem is time-consuming to solve. [ABSTRACT FROM AUTHOR]

This paper presents a convex mathematical programming model for the global optimization of recycle/reuse water networks. The model is based on a general superstructure that includes the major configurations of interest such as segregation, mixing, recycle, bypass, and treatment of streams needed to satisfy the process and environmental constraints. The basic idea of the model formulation is to consider component balances, treating as optimization variables the individual flowrates. This formulation avoids the bilinear terms that appear when the compositions and total flowrates are considered as optimization variables. The objective function consists in the minimization of the total annual cost including the fresh sources costs, the treatment units costs (which are reformulated as convex functions) and the piping costs. Four examples problems are solved to show the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the stability of the sets of efficient points of vector-valued optimization problems when the data of the approximate problems converges to the data of the original problem in the sense of Painlevé-Kuratowski. Our results improve the corresponding results obtained by Lucchetti and Miglierina (Optimization 53(5-6):517-528, , Section 3). [ABSTRACT FROM AUTHOR]

For 30 years after their invention half a century ago, cutting planes for integer programs have been an object of theoretical investigations that had no apparent practical use. When they finally proved their practical usefulness in the late eighties, that happened in the framework of branch and bound procedures, as an auxiliary tool meant to reduce the number of enumerated nodes. To this day, pure cutting plane methods alone have poor convergence properties and are typically not used in practice. Our reason for studying them is our belief that these negative properties can be understood and thus remedied only based on a thorough investigation of such procedures in their pure form. In this paper, the second in a sequence, we address some important issues arising when designing a computationally sound pure cutting plane method. We analyze the dual cutting plane procedure proposed by Gomory in 1958, which is the first (and most famous) convergent cutting plane method for integer linear programming. We focus on the enumerative nature of this method as evidenced by the relative computational success of its lexicographic version (as documented in our previous paper on the subject), and we propose new versions of Gomory's cutting plane procedure with an improved performance. In particular, the new versions are based on enumerative schemes that treat the objective function implicitly, and redefine the lexicographic order on the fly to mimic a sound branching strategy. Preliminary computational results are reported. [ABSTRACT FROM AUTHOR]

The present paper studies the following constrained vector optimization problem: $$\mathop {\min }\limits_C f(x),g(x) \in - K,h(x) = 0$$, where f: ℝ n → ℝ m, g: ℝ n → ℝ p are locally Lipschitz functions, h: ℝ n → ℝ q is C1 function, and C ⊂ ℝ m and K ⊂ ℝ p are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x0 to be a w-minimizer and first-order sufficient conditions for x0 to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done. [ABSTRACT FROM AUTHOR]

In this paper, properties of the entropic risk measure are examined rigorously in a general framework. This risk measure is then applied in a dynamic portfolio optimization problem, appearing in the risk management constraint. By considering the dual problem, we prove the existence and uniqueness of the solution and obtain an analytic expression for the solution. [ABSTRACT FROM AUTHOR]

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\mathcal {J}(u)=\int_{\partial\Omega}f(x)u\,\mathrm {d}\mathcal {H}^{N-1}$ over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+| u| p−2 u=0 in Ω with | ∇ u| p−2 u ν= f on ∂Ω. [ABSTRACT FROM AUTHOR]

Proximal-point algorithms (PPAs) are classical solvers for convex optimization problems and monotone variational inequalities (VIs). The proximal term in existing PPAs usually is the gradient of a certain function. This paper presents a class of PPA-based methods for monotone VIs. For a given current point, a proximal point is obtained via solving a PPA-like subproblem whose proximal term is linear but may not be the gradient of any functions. The new iterate is updated via an additional slight calculation. Global convergence of the method is proved under the same mild assumptions as the original PPA. Finally, profiting from the less restrictions on the linear proximal terms, we propose some parallel splitting augmented Lagrangian methods for structured variational inequalities with separable operators. [ABSTRACT FROM AUTHOR]

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]

An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field, which in turn defines a system of ordinary differential equations (ODEs). The solutions of the system of ODEs are called off-central paths, underlying paths lying in the interior of the feasible region. It is known that not all off-central paths are analytic, whether w.r.t. μ or $\sqrt{\mu}$ , where μ represents the duality gap, at a solution of a given semidefinite linear complementarity problem, SDLCP (Sim and Zhao, Math. Program. 110:475–499, ). In Sim and Zhao (J. Optim. Theory Appl. 137:11–25, ), we give a necessary and sufficient condition for when an off-central path is analytic as a function of $\sqrt{\mu}$ at a solution of a general SDLCP. It is then natural to ask about the analyticity of a SDLCP off-central path at a solution, as a function of μ. We investigate this in the current paper. Again, we work under the assumption that the given SDLCP satisfies strict complementarity condition. [ABSTRACT FROM AUTHOR]

We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization. [ABSTRACT FROM AUTHOR]

An optimization problem is defined by an objective function to be maximized with respect to a set of constraints. To overcome some theoretical and practical difficulties, the constraint-set is sometimes relaxed and “easier” problems are solved. This led us to study relaxations providing exactly the same set of optimal solutions. We give a complete characterization of these relaxations and present several examples. While the relaxations introduced in this paper are not always easy to solve, they may help to prove that some mathematical programs are equivalent in terms of optimal solutions. An example is given where some of the constraints of a linear program can be relaxed within a certain limit. [ABSTRACT FROM AUTHOR]

This paper examines a number of variants of the sparse k-spanner problem and presents hardness results concerning their approximability. Previously, it was known that most k-spanner problems are weakly inapproximable (namely, they are NP-hard to approximate with ratio O(log n), for every k ≥ 2) and that the unit-length k-spanner problem for constant stretch requirement k ≥ 5 is strongly inapproximable (namely, it is NP-hard to approximate with ratio $O(2^{{\log}^{1 - \epsilon} n})$ ). The results of this paper significantly expand the ranges of hardness for k-spanner problems. In general, strong hardness is shown for a number of k-spanner problems, for certain ranges of the stretch requirement k depending on the particular variant at hand. The problems studied differ by the types of edge weights and lengths used, and they include directed, augmentation and client-server variants. The paper also considers k-spanner problems in which the stretch requirement k is relaxed (e.g., $k = \Omega(\log n))$ . For these cases, no inapproximability results were known (even for a constant approximation ratio) for any spanner problem. Moreover, some versions of the k-spanner problem are known to enjoy the ratio-degradation property; namely, their complexity decreases exponentially with the inverse of the stretch requirement. So far, no hardness result existed precluding any k-spanner problem from enjoying this property. This paper establishes strong inapproximability results for the case of relaxed stretch requirement (up to $k = O(n^{{1 - \delta}})$ , for any $0 < \delta < 1$ ), for a large variety of k-spanner problems. It is also shown that these problems do not enjoy the ratio-degradation property. [ABSTRACT FROM AUTHOR]

This paper studies the problem of maximizing the number of correct results of dependent tasks computed unreliably. We consider a distributed system composed of a reliable server that coordinates the computation of a massive number of unreliable workers. Any worker computes correctly with probability p < 1. Any incorrectly computed task corrupts all dependent tasks. The goal is to determine which tasks should be computed by the (reliable) server and which by the (unreliable) workers, and when, so as to maximize the expected number of correct results, under a constraint d on the computation time. This problem is motivated by distributed computing applications that persist partial results of computations for future use in other computations and that want to ensure that the persisted results are of high quality. We show that this optimization problem is NP-hard. Then we study optimal scheduling solutions for the mesh with the tightest deadline. We present combinatorial arguments that describe all optimal solutions for two ranges of values of worker reliability p, when p is close to zero and when p is close to one. [ABSTRACT FROM AUTHOR]

Due to the large amounts of data required to be processed by the typical Grid job, it is conceivable that the use of optical transport networks in Grid deployment (hence the term “Lambda Grid”) will increase. The exact topology of the interconnecting network is obtained by solving a dimensioning problem, and the outcome of this strongly depends on both the expected workload characteristics and Grid scheduling policy. Solving this combined scheduling and dimensioning problem using straightforward ILP modelling is cumbersome; however, for steady-state Grid operation, Divisible Load Theory (DLT) can yield scalable formulations of this problem. In this paper, the on-line hierarchical scheduling on a lambda Grid of workload approaching the Grid’s capacity in a two-tier Grid mode of operation is studied. A number of these algorithms are goal-driven, in the sense that target per-resource goals are obtained from the off-line solution to the Divisible Load model. We compare these on-line multiresource scheduling policies for different workloads, Grid interconnection topologies and Grid parameters. We show that these algorithms perform well in the studied scenarios when compared to a fully centralized scheduling algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the stabilization problem for a class of linear nonautonomous systems with norm-bounded controls. Using the Lyapunov function technique, we establish simple verifiable stabilizability conditions without solving any Riccati differential equation. Numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to pose and solve a simple class of coordinated motion problems that capture the following question; When is formation travel optimal? This class of problems is complementary to two related classes of problems that have received significant attention: close formation travel and the generation of flocking behavior. We pose and solve this problem for the case of two agents traversing a finite, connected graph. Two examples are provided, illustrating the application of the results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set. The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper. the design problem of the dynamic output feedback controller for the asymptotic stabilization of a class of linear delay differential systems of the neutral type is considered. A criterion for the existence of such controller is derived based on the matrix inequality approach combined with the Lyapunov method. A parametrized characterization of the controller is given in terms of the feasible solutions to certain matrix inequalities, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed design method. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new robust FIR equalizer for discrete time systems subject to parameter uncertainties in the matrices of the system state-space model from an H8 perspective. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The discrete algebraic Riccati inequality (DARI) and linear matrix inequality (LMI) provide an extremely superior methodology in the H8 control fields. By the H8 and robust methods in conjunction with the bounded real lemma, the robust FIR equalizer design is transformed into a standard LMI optimization problem. An example is given to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

A discrete filled function method is developed in this paper to solve discrete global optimization problems over ‘strictly pathwise connected domains.’ Theoretical properties of the proposed discrete filled function are investigated and a solution algorithm is proposed. Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the applicability and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of a differential inclusion built upon a nonsmooth, not necessarily convex, constrained minimization problem in finite-dimensional spaces. In particular, we are interested in the investigation of the asymptotic behavior of the trajectories of the dynamical system represented by the differential inclusion. Under suitable assumptions on the constraint set and the two involved functions (one defining the constraint set, the other representing the functional to be minimized), it is proved that all the trajectories converge to the set of the constrained critical points. We present also a large class of constraint sets satisfying our assumptions. As a simple consequence. in the case of a smooth convex minimization problem, we have that any trajectory converges to the set of minimizers. [ABSTRACT FROM AUTHOR]

Mathematical programs with equilibrium constraints (MPEC) are nonlinear programs which do not satisfy any of the common constraint qualifications (CQ). In order to obtain first-order optimality conditions, constraint qualifications tailored to the MPECs have been developed and researched in the past. In this paper. we introduce a new Abadie-type constraint qualification for MPECs. We investigate sufficient conditions for this new CQ. discuss its relationship to several existing MPEC constraint qualifications, and introduce a new Slater-type constraint qualifications. Finally, we prove a new stationarity concept to be a necessary optimality condition under our new Abadie-type CQ. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonmonotone trust-region algorithm for the solution of optimization problems with general nonlinear equality constraints and simple bounds. Under a constant rank assumption on the gradients of the active constraints, we analyze the global convergence of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets. [ABSTRACT FROM AUTHOR]

General closed-loop performance optimization problems with pole assignment constraint are considered in this paper under a unified framework. By introducing a free-parameter matrix and a matrix function based on the solution of a Sylvester equation, the constrained optimization problem is transformed into an unconstrained one, thus reducing the problem of closed-loop performance optimization with pole placement constraint to the computation of the gradient of the performance index with respect to the free-parameter matrix. Several classical performance indices are then optimized under the pole placement constraint. The effectiveness of the proposed gradient method is illustrated with an example. [ABSTRACT FROM AUTHOR]

In this paper, optimality conditions are presented and analyzed for the cardinality-constrained cone programming arising from finance, statistical regression, signal processing, etc. By introducing a restricted form of (strict) Robinson constraint qualification, the first-order optimality conditions for the cardinality-constrained cone programming are established based upon the properties of the normal cone. After characterizing further the second-order tangent set to the cardinality-constrained system, the second-order optimality conditions are also presented under some mild conditions. These proposed optimality conditions, to some extent, enrich the optimization theory for noncontinuous and nonconvex programming problems. [ABSTRACT FROM AUTHOR]

This paper describes a novel approach for solving combinatorial optimisation problems called Simulated Jumping. It is based on ideas from spin-glasses, simulated annealing and self-organisation. We start from a low temperature, and the system is then subjected to a rapid heating and cooling process (a shaking process). This process is controlled by the system's energy in a self-organised manner. The heating and cooling process will continuously melt and freeze local regions; this process pushes the system out of local minima and hence minimises the energy function. Application of the Simulated Jumping method to the Quadratic Assignment and Asymmetric Travelling Salesman problems gives promising results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with an algorithm which combines the generalized linear programming technique proposed by Dantzig and Wolfe with the stochastic quasi-gradient method in order to solve stochastic programs with recourse. In this way, we overcome the difficulties arising in finding the exact values of the objective function of recourse problems by replacing them with the statistical estimates of the function. We present the basic steps of the proposed algorithm focusing our attention on its implementation alternatives aimed at improving both the convergence and computational performances. The main application areas are mentioned and some computational experience in the validation of our approach is reported. Finally, we discuss the possibilities of parallelization of the proposed algorithmic schemes. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding minimal length tree networks on the unit sphere Φ of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal Tree SMT (V) and of finding a Minimum Spanning Tree MST(V) are treated through a simplicial decomposition technique based on computing the Delaunay Triangulation DT (V) and the Voronoi Diagram VD(V) of the given point set. O (N log N) algorithms for computing DT(V), VD(V), and WST(V) as well as an O(N log N) heuristic for finding a sub-optimal SMT(V) solution are presented, together with experimental results for randomly distributed points on Φ. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to give a survey of methods, partly derived by the author in joint work with other researchers, concerning the problem of constructing e-optimal strategies for partially observable MDPs. The methods basically consist in transforming the problem into one of approximation: Starting from the original problem a sequence of approximating problems is constructed such that: (i) For each approximating problem an optimal strategy can actually be computed, (ii) Given ϵ » 0, there exists an approximating problem such that the optimal strategy for the latter is ϵ-optimal for the original problem. [ABSTRACT FROM AUTHOR]

In this paper we discuss optimality-based domain reductions for Global Optimization problems both from the theoretical and from the computational point of view. When applying an optimality-based domain reduction we can easily define a lower limit for the reduction which can be attained, but we can hardly guarantee that such limit is reached. Here, we theoretically prove that, for a nontrivial class of problems, appropriate strategies exist that are always able to reach this lower limit. On the other hand, we will also show that the same strategies lose this property as soon as we slightly enlarge the class of problems. Next, we perform computational experiments with a standard B&B approach applied to Linear Multiplicative Programming problems. We aim at establishing a good trade off between the quality of the domain reduction (the higher the quality, the lower the number of nodes in the B&B tree), and the computational cost of the domain reduction, and, thus, the effort per node of the B&B tree. [ABSTRACT FROM AUTHOR]