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作者：Chen, XJ; Fukushima, M
作者单位：Hirosaki University; Kyoto University
摘要：This paper presents a new formulation for the stochastic linear complementarity problem (SLCP), which aims at minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and prove that every accumulation point of minimizers of discrete approximation problems is a minimum expected residual solution of the SLCP. We show that a sufficient condition for the existence of a solution to the expected residual minimization (ERM) problem and its ...
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作者：Tao, JY; Gowda, MS
作者单位：Loyola University Maryland; University System of Maryland; University of Maryland Baltimore County
摘要：In this article, we introduce the concepts of P and P-0 properties for a nonlinear transformation defined on a Euclidean Jordan algebra and study existence of solution in the associated complementarity problems. In particular, we show, in this general setting, that if a transformation has the P-0 and R-0 properties, then all associated complementarity problems have solutions. We also describe a necessary condition for a transformation to have Lie (global) uniqueness of solution property.
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作者：Mordukhovich, BS; Nam, NM
作者单位：Wayne State University
摘要：Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimization. We develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative calculus for set-valued mappings and singular subdifferentials of marginal functions in infinite dimens...
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作者：Décamps, JP; Mariotti, T; Villeneuve, S
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; University of London; London School Economics & Political Science
摘要：We study the decision of when to invest in a project whose value is perfectly observable but driven by a parameter that is unknown to the decision maker ex ante. This problem is equivalent to an optimal stopping problem for a bivariate Markov process. Using filtering and martingale techniques, we show that the optimal investment region is characterized by a continuous and nondecreasing boundary in the value-belief state space. This generates path-dependency in the optimal investment strategy. ...
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作者：Chiarolla, MB; Haussmann, UG
作者单位：Sapienza University Rome; University of British Columbia
摘要：We consider a firm producing a single consumption good that makes irreversible investments to expand its production capacity. The firm aims to maximize its expected total discounted real profit net of investment on a finite horizon T. The capacity is modeled as a controlled Ito process where the control is the real investment, which is not necessarily a rate, but more generally a monotone process. The result is a singular stochastic control problem. We introduce the associated optimal stopping...
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作者：Alvarez, F; Carrasco, M; Pichard, K
作者单位：Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a general hybrid iterative algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis...
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作者：Dokov, SP; Morton, DP
作者单位：University of Texas System; University of Texas Austin
摘要：We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyperrectangle. Our bounds have applications to stochastic programs whose random parameters are known only through limited-moment information. Computational results are presented for two-stage stochastic linear programs.
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作者：Shapiro, A
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：In this paper we discuss local uniqueness, continuity, and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use two types of techniques. One approach consists in formulating variational inequalities in a form of optimization problem based on regularized gap functions, and applying a general theory of perturbation analysis of parameterized optimization problems. Another approach is based on a theory of contingent (outer ...
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作者：Einstein, O; Hassin, R
作者单位：Tel Aviv University; Tel Aviv University
摘要：This paper deals with families of optimization problems defined over a common set of potential solutions. We consider several problems-solutions systems, and for each one, prove the existence of a small set of solutions that contains an optimal solution to every problem. These proofs are mostly algebraic in nature. The families of problems covered here mostly include separation problems, problems on graphs and hypergraphs, and SAT problems.
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作者：Levy, AB
作者单位：Bowdoin College
摘要：Successive approximation methods appear throughout numerical optimization, where a solution to an optimization problem is sought as the limit of solutions to a succession of simpler approximation problems. Such methods include essentially any standard penalty method, barrier method, trust region method, augmented Lagrangian method, or sequential quadratic programming (SQP) method, as well as many other methods. The approximation problems on which a successive approximation method is based typi...
