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In this paper, we consider a constrained nonconvex nonsmooth optimization, in which both objective and constraint functions may not be convex or smooth. With the help of the penalty function, we transform the problem into an unconstrained one and design an algorithm in proximal bundle method in which local convexification of the penalty function is utilized to deal with it. We show that, if adding a special constraint qualification, the penalty function can be an exact one, and the sequence generated by our algorithm converges to the KKT points of the problem under a moderate assumption. Finally, some illustrative examples are given to show the good performance of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique. [ABSTRACT FROM AUTHOR]

In real linear spaces, partial orderings are usually generated by ordering cones. In many situations, however, such an ordering cone is too small with respect to the whole space. Therefore, in this paper, we extend the concept of ordering cones to a more general concept. For this purpose, we define a parameterized binary relation, based on a convex cone and a binary function. We investigate some geometrical and topological properties of this relation in detail. [ABSTRACT FROM AUTHOR]

The indispensability argument seeks to establish the existence of mathematical objects. The success of the indispensability argument turns on finding cases of genuine extra-mathematical explanation (the explanation of physical facts by mathematical facts). In this paper, I identify a new case of extra-mathematical explanation, involving the search patterns of fully-aquatic marine predators. I go on to use this case to predict the prevalence of extra-mathematical explanation in science. [ABSTRACT FROM AUTHOR]

This article presents a family of semidefinite programming bounds, obtained by Lagrangian duality, for 0-1 quadratic optimization problems with linear or quadratic constraints. These bounds have useful computational properties: they have a good ratio of tightness to computing time, they can be optimized by a quasi-Newton method, and their final tightness level is controlled by a real parameter. These properties are illustrated on three standard combinatorial optimization problems: unconstrained 0-1 quadratic optimization, heaviest $$k$$-subgraph, and graph bisection. [ABSTRACT FROM AUTHOR]

In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of discussed theory is presented. It concerns the system with a PD-controller designed to control a plant with two delays both retarded and neutral type. For such system a value of considered performance index is determined. [ABSTRACT FROM AUTHOR]

During the last years several ant-based techniques were involved to solve hard and complex optimization problems. The current paper is a short study about the influence of artificial ant species in solving optimization problems. There are studied the artificial Pharaoh Ants, Lasius Niger and also artificial ants with no special specificity used commonly in Ant Colony Optimization. [ABSTRACT FROM AUTHOR]

The single-row facility layout problem (SRFLP) is an NP-hard combinatorial optimization problem that is concerned with the arrangement of n departments of given lengths on a line so as to minimize the weighted sum of the distances between department pairs. (SRFLP) is the one-dimensional version of the facility layout problem that seeks to arrange rectangular departments so as to minimize the overall interaction cost. This paper compares the different modelling approaches for (SRFLP) and applies a recent SDP approach for general quadratic ordering problems from Hungerländer and Rendl to (SRFLP). In particular, we report optimal solutions for several (SRFLP) instances from the literature with up to 42 departments that remained unsolved so far. Secondly we significantly reduce the best known gaps and running times for large instances with up to 110 departments. [ABSTRACT FROM AUTHOR]

SUMMARY Structural identification based on analysis of vibration signals is usually formulated as an optimization problem. Nevertheless, identifying a structural system as a whole often involves a great number of unknowns and degrees of freedom, resulting in considerable convergence difficulty and expensive evaluation of objective function. To handle these issues, this paper aims to propose a frequency domain substructural identification method applicable to arbitrary excitations. This is done by introducing the exponential window method in the formulation so that the effect caused by initial condition is alleviated without using zero padding. The proposed identification method is verified through both numerical and experimental studies. It is shown that significant reduction in computer time can be achieved in addition to remarkable identification accuracy. The experimental study also indicates that the proposed strategy is effective in identifying small structural changes. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. - and -type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the -stationarity conditions. [Copyright &y& Elsevier]

In this paper, the concept of second order generalized α-type I univexity is introduced. Based on the new definitions, we derive weak, strong and strict converse duality results for two second order duals of a minmax fractional programming problem. [ABSTRACT FROM AUTHOR]

Abstract: this paper gives them some properties. This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper not only gives them some properties, but also analyze the time complexity of it. [Copyright &y& Elsevier]

Abstract: This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper gives them somae properties. [Copyright &y& Elsevier]

Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonlinear programming, and variational inequalities. We will describe the modeling approaches, mathematical formulations, and recent results of these paradigms, and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems. Our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field. [ABSTRACT FROM AUTHOR]

The Fermat-Torricelli problem is an optimization problem associated with a finite subset $\{a_{j}\}_{j=1}^{q}$ of ℝ and a family $\{c_{j}\}_{j=1}^{q}$ of positive weights. The function F to be minimized is defined by $F(x)=\sum _{j=1}^{q}c_{j}\Vert x-a_{j}\Vert$. In this paper, we extend this problem to the case of volumes. [ABSTRACT FROM AUTHOR]

In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst. [ABSTRACT FROM AUTHOR]

In this paper a new hybrid conjugate gradient algorithm is proposed and analyzed. The parameter β k is computed as a convex combination of the Polak-Ribière-Polyak and the Dai-Yuan conjugate gradient algorithms, i.e. β=(1− θ k) β+ θ k β. The parameter θ k in the convex combination is computed in such a way that the conjugacy condition is satisfied, independently of the line search. The line search uses the standard Wolfe conditions. The algorithm generates descent directions and when the iterates jam the directions satisfy the sufficient descent condition. Numerical comparisons with conjugate gradient algorithms using a set of 750 unconstrained optimization problems, some of them from the CUTE library, show that this hybrid computational scheme outperforms the known hybrid conjugate gradient algorithms. [ABSTRACT FROM AUTHOR]

Let X be a partially ordered real Banach space, let a, b∈ X with a≤ b. Let φ be a bounded linear functional on X. We say that X satisfies the box-optimization property (or X is a BOP space) if the box-constrained linear program: max 〈 φ, x〉, s.t. a≤ x≤ b, has an optimal solution for any φ, a and b. Such problems arise naturally in solving a class of problems known as interval linear programs. BOP spaces were introduced (in a different language) and systematically studied in the first author’s doctoral thesis. In this paper, we identify new classes of Banach spaces that are BOP spaces. We present also sufficient conditions under which answers are in the affirmative for the following questions: [ABSTRACT FROM AUTHOR]

The notion of extended-well-posedness has been introduced by Zolezzi for scalar minimization problems and has been further generalized to vector minimization problems by Huang. In this paper, we study the extended well-posedness properties of vector minimization problems in which the objective function is C-quasiconvex. To achieve this task, we first study some stability properties of such problems. [ABSTRACT FROM AUTHOR]

The article explores the mechanics of the television game show "The Weakest Link." Contestants of the game answer general knowledge questions, with each correct answer raising the amount held in a temporary pot. The game involves several mathematical issues such as strategy optimization, existence of Nash equilibria, and voting considerations. The payoff vector as being the amount in the pot after a chain of correct answers was introduced to describe various versions of the game around the world.

This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L p . It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L ∞-setting is analyzed, but also a more involved L q -analysis, q < ∞, is presented. In L ∞, the set of feasible controls contains interior points and the Fréchet differentiability of the perturbed optimality system can be shown. In the L q -setting, which is highly relevant for PDE-constrained optimization, these nice properties are no longer available. Nevertheless, a convergence analysis is developed using refined techniques. In parti- cular, two-norm techniques and a smoothing step are required. The L q -analysis with smoothing step yields global linear and local superlinear convergence, whereas the L ∞-analysis without smoothing step yields only global linear convergence. [ABSTRACT FROM AUTHOR]

In this paper we study some second order conditions that may be added to the first order nessessary optimality condition 0 ∈ ∂p&fnop;(¯X) (with ∂pƒ denoting the proximal subdifferential) in order to obtain a sufficient condition for a strict local minimum for extended--real-valued, nonsmooth functions. Three different types of second order conditions are investigated, all based on a different second order subdifferential. Namely, the subhessian, the graphical derivative, and the (contingent) coderivative to the proximal subdifferential. [ABSTRACT FROM AUTHOR]

In this paper, we derive some existence results for generalized variational inequalities associated with mappings satisfying the ( S)+ condition. The relation between the ( S)+ and ( S) conditions is discussed. As an application, we also consider multivalued complementarity problems associated with mappings satisfying the ( S)+ condition, and prove a theorem to characterize the solvability of such problems in terms of exceptional families of elements. [ABSTRACT FROM AUTHOR]

In this paper, following the method in the proof of the composition duality principle due to Robinson and using some basic properties of the ε-subdifferential and the conjugate function of a convex function, we establish duality results for an ε-variational inequality problem. Then, we give Fenchel duality results for the ε-optimal solution of an unconstrained convex optimization problem. Moreover, we present an example to illustrate our Fenchel duality results for the ε-optimal solutions. [ABSTRACT FROM AUTHOR]

The question of determining strong convex underestimators for nonlinear functions is theoretically and practically of major interest. Unfortunately, results along these lines are quite limited as very few general procedures are at hand that can be applied to general classes of functions. In this paper we show how to reduce the question of determining a convex envelope to lower-dimensional optimization problems when the underlying function is indefinite and (n-1)-convex. Our structural result about this reduction technique enables us to give descriptions for the convex envelope of a variety of two-dimensional functions. [ABSTRACT FROM AUTHOR]

Abstract  This paper describes a new multiobjective interactive memetic algorithm applied to dynamic location problems. The memetic algorithm integrates genetic procedures and local search. It is able to solve capacitated and uncapacitated multi-objective single or multi-level dynamic location problems. These problems are characterized by explicitly considering the possibility of a facility being open, closed and reopen more than once during the planning horizon. It is possible to distinguish the opening and reopening periods, assigning them different coefficient values in the objective functions. The algorithm is part of an interactive procedure that asks the decision maker to define interesting search areas by establishing limits to the objective function values or by indicating reference points. The procedure will be applied to some illustrative location problems. [ABSTRACT FROM AUTHOR]

In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute non-parametric M-estimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the ‘Aspect problem’ in quantum physics. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a new type of the classical Bernstein operators where the function is evaluated at intervals . We also make extensive study simultaneous approximation by the linear combination of these new Bernstein type operators . At the end of this paper we have given an other modification of these operators. [Copyright &y& Elsevier]

Abstract: Ecological expert knowledge is often based on qualitative rules consisting of linguistic terms such as ‘low’, ‘moderate’ or ‘high’. Since fuzzy systems transform these rules and terms into a mathematical framework, they allow implementing this expert knowledge in ecological models. However, the development of a reliable knowledge base is complex and time consuming. Recent research has shown that complementing fuzzy systems by data-driven techniques can solve this knowledge acquisition bottleneck. In this paper, a heuristic nearest ascent hill-climbing algorithm for rule base optimisation is applied to construct a fuzzy rule-based habitat suitability model for spawning European grayling (Thymallus thymallus L.) in the Aare river (Bern, Switzerland). Optimisation of the fuzzy rule-based model was based on two different training criteria, the weighted correctly classified instances and Cohen''s Kappa. The ecological relevance of the results was assessed by comparing the optimised rule bases with a rule base derived from ecological expert knowledge. Optimisation based on Kappa appeared to generate acceptable results (CCI=0.70; Kappa=0.32) and was more practical than optimisation based on since the latter required fine tuning of a weight parameter, which accounted for the species prevalence. The optimal rules showed 74% similarity with the rules derived from expert knowledge, while 84% of all model errors was due to false positive predictions of the model. These errors might be due to the impact of variables, which were not included in this study on grayling presence and thus are not necessarily a model error. The habitat suitability model optimised in this paper is able to predict the effect of different impacts on the river system and to select the optimal restoration option. Hence, it could be a valuable decision support tool for river managers and ease the discussion between stakeholders. [Copyright &y& Elsevier]

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the triality theory associated with the canonical duality theory. Several examples are illustrated. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to establish the second-order nonsmooth sufficient unconstrained optimality condition for so called ℓ-stable at some point functions and in this way to generalize some previous results in this direction. We provide the comparisons with other results by examples. [ABSTRACT FROM AUTHOR]

It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this paper a modified trust-region method with Beale's Preconditioned Conjugate Gradient (BPCG) technique is developed for solving unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties are discussed. Some numerical experiments are reported. [ABSTRACT FROM AUTHOR]

Let M be a matroid on E υ {l}, where l ∉ E is a distinguished element of M, The l-port of M is the set 풫 = {P: P ⊆ E with P υ {l} a circuit of M}. Let A be the 풫-E incidence matrix. Let U2,4 be the uniform matroid on four elements of rank two, let F7 be the Fano matroid, let F7* be the dual of F7, and let F7+ be the unique series extension of F7. In this paper, we prove that the system Ax ≥ 1, x ≥ 0 is box-totally dual integral (box-TDI) if and only if M has no U2.4-minor using l, no F7*-minor using l, and no F7+-minor using l as a series element. Our characterization yields a number of interesting results in combinatorial optimization. [ABSTRACT FROM AUTHOR]

A key challenge in using timing-robust asynchronous circuit styles is the lack of automated optimization techniques. In this paper, technology mapping and cell merger algorithms for asynchronous threshold networks are introduced. The cell merger problem is a restricted form of technology mapping where only adjacent cells are merged. The two algorithms can each target either delay or area, or a combined delay-area cost function. Experiments were performed on substantial industrial design examples (DES and GCD circuits) that had already been optimized by an existing commercial asynchronous synthesis tool flow. Average delay improvements of 31.6% for basic technology mapping and 29.6% for basic cell merger were obtained. Average area improvements of 9.5 % for basic technology mapping and 8.5 % for basic cell merger were also obtained. Additional experiments were performed on the largest MCNC combinational benchmarks with similar results. Finally, targeting a hybrid cost function, area minimization under specified hard timing constraints, a further area reduction of up to 10.7% on average in technology mapping was recovered without compromising the overall system performance. The new algorithms are the first systematic and general mapping approach for asynchronous threshold networks, targeting delay or area, which preserve the timing-robustness properties of the initial unoptimized circuits. [ABSTRACT FROM AUTHOR]

During the last years nature inspired intelligent techniques have become attractive for analyzing large data sets and solving complex optimization problems. In this paper, one of the most interesting of them, the Ant Colony Optimization (ACO), is used for the construction of a hybrid algorithmic scheme which effectively handles the Pap Smear Cell classification problem. This algorithmic approach is properly combined with a number of nearest neighbor based approaches for performing the requested classification task, through the solution of the so-called optimal feature subset selection problem. The proposed complete algorithmic scheme is tested in two sets of data. The first one consists of 917 images of pap smear cells and the second set consists of 500 images, classified carefully by expert cyto-technicians and doctors. Each cell is described by 20 numerical features, and the cells fall into seven (7) classes, four (4) representing normal cells and three (3) abnormal cases. Nevertheless, from the medical diagnosis viewpoint, a minimum requirement corresponds to the general two-class problem of correct separation between normal from abnormal cells. [ABSTRACT FROM AUTHOR]

In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention. [ABSTRACT FROM AUTHOR]

It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper, a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly feasible points in both the primal and dual spaces can be defined. A second benefit of the modification is an improvement in the complexity analysis of conic cutting surface algorithms. Complexity results for conic cutting surface algorithms proved to date have depended on a condition number of the added constraints. The proposed modification of the constraints leads to a stronger result, with the convergence of the resulting algorithm not dependent on the condition number. [ABSTRACT FROM AUTHOR]

The effective resistance between two nodes of a weighted graph is the electrical resistance seen between the nodes of a resistor network with branch conductances given by the edge weights. The effective resistance comes up in many applications and fields in addition to electrical network analysis, including, for example, Markov chains and continuous-time averaging networks. In this paper we study the problem of allocating edge weights on a given graph in order to minimize the total effective resistance, i.e., the sum of the resistances between all pairs of nodes. We show that this is a convex optimization problem and can be solved efficiently either numerically or, in some cases, analytically. We show that optimal allocation of the edge weights can reduce the total effective resistance of the graph (compared to uniform weights) by a factor that grows unboundedly with the size of the graph. We show that among all graphs with n nodes, the path has the largest value of optimal total effective resistance and the complete graph has the least. [ABSTRACT FROM AUTHOR]

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see http://www.optimization-online.org/DB_HTML/2005/02/1056.html). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems. [ABSTRACT FROM AUTHOR]

Any Boolean function can be defined by a Boolean circuit, provided we may use sufficiently strong functions in its gates. On the other hand, what Boolean functions can be defined depends on these gate functions: Each set B of gate functions defines the class of Boolean functions that can be defined by circuits over B. Although these classes have been known since the 1920s, their computational complexity was never investigated. In this paper we will study how difficult it is to decide for a Boolean function f and a class B, whether f is in B. Moreover, we will provide such a decision algorithm with additional information: How difficult is it to decide whether or not f is in B, provided we already know a circuit for f, but with gates from another class A? Given such a circuit, we know that f is in A. Is the problem harder if we do not have a concrete representation for f, but still know that it is from A? For nearly all possible combinations, we show that this is not the case, and that the problem is either in P or coNP-complete. [ABSTRACT FROM AUTHOR]

We introduce new data structures for compressed suffix trees whose size are linear in the text size. The size is measured in bits; thus they occupy only O(n log|A|) bits for a text of length n on an alphabet A. This is a remarkable improvement on current suffix trees which require O(n log n) bits. Though some components of suffix trees have been compressed, there is no linear-size data structure for suffix trees with full functionality such as computing suffix links, string-depths and lowest common ancestors. The data structure proposed in this paper is the first one that has linear size and supports all operations efficiently. Any algorithm running on a suffix tree can also be executed on our compressed suffix trees with a slight slowdown of a factor of polylog(n). [ABSTRACT FROM AUTHOR]

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer and Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim [image omitted] , where H is the payoff of the claim and [image omitted] is a solution of the static optimization problem, an optimal randomized test. In this paper, necessary and sufficient optimality conditions are deduced for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1-structure. [ABSTRACT FROM AUTHOR]

Direct search optimization algorithms are becoming an important alternative to well-established gradient based methods. Due to the fact that a single cost function evaluation may take a substantial amount of time, optimization can be a lengthy process. In order to shorten the run time one often resorts to parallel algorithms. Asynchronous algorithms are particularly efficient since they have no synchronization points. This paper is an attempt to establish a convergence theory for a class of such parallel direct search algorithms. The notion of a search direction generator (SDG) is introduced. An algorithmic framework for parallel distributed optimization methods based on SDGs is presented along with the corresponding convergence theory. The theory almost completely decouples the stepsize control from the sufficient descent requirement, which is necessary for the finite termination of the algorithm's inner loop. The proposed framework has several attributes considered very favourable in loosely coupled parallel systems (e.g. clusters of workstations), such as fault tolerance and scalability. The framework is illustrated by optimizing a set of test problems on a cluster of workstations. In all tested cases, a speedup was obtained that increased with the increasing number of workstations. Fault tolerance and scalability of the framework were also demonstrated by removing and adding workstations to the cluster while an optimization run was in progress. [ABSTRACT FROM AUTHOR]

Iterative solvers appear to be very promising in the development of efficient software, based on Interior Point methods, for large-scale nonlinear optimization problems. In this paper we focus on the use of preconditioned iterative techniques to solve the KKT system arising at each iteration of a Potential Reduction method for convex Quadratic Programming. We consider the augmented system approach and analyze the behaviour of the Constraint Preconditioner with the Conjugate Gradient algorithm. Comparisons with a direct solution of the augmented system and with MOSEK show the effectiveness of the iterative approach on large-scale sparse problems. [ABSTRACT FROM AUTHOR]

In this paper, we present new convergence properties of the primal-dual method based on four types of augmented Lagrangian functions in the context of constrained global optimization. Convergence to a global optimal solution is first established for a basic primal-dual scheme under standard conditions. We then prove this convergence property for a modified augmented Lagrangian method using a safeguarding strategy without appealing to the boundedness assumption of the multiplier sequence. We further show that, under the same weaker conditions, the convergence to a global optimal solution can still be achieved by either modifying the multiplier updating rule or normalizing the multipliers in augmented Lagrangian methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right-hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts. [ABSTRACT FROM AUTHOR]

In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints. [ABSTRACT FROM AUTHOR]

The background for this article is the question of modification of the geometric configuration of an elastic structure by means of "volume"-type actuation. In this actuation mode stresses are applied to the elastic body by injection/extraction of a fluid into, or from, a large number of vacuoles in the elastic "matrix" material. Previous articles by the author, and others, have examined this process and studied its effectiveness in the context of a "naive" continuous model. The present paper develops modified models in the two-dimensional case by applying the "multiple scales" homogenization method to elastic bodies with increasingly small and numerous vacuoles arranged in a rectangularly periodic structure. The process leads to a modification of the naive model potentially useful in future elastic system control research. [ABSTRACT FROM AUTHOR]

Abstract??In this paper, we consider Levitin?Polyak type well-posedness for a general constrained vector optimization problem. We introduce several types of (generalized) Levitin?Polyak well-posednesses. Criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods under the assumption of a type of generalized Levitin?Polyak well-posedness. [ABSTRACT FROM AUTHOR]