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作者：Burer, Samuel; Kilinc-Karzan, Fatma
作者单位：University of Iowa; Carnegie Mellon University
摘要：A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonc...
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作者：Basu, Amitabh; Martin, Kipp; Ryan, Christopher Thomas
作者单位：Johns Hopkins University; University of Chicago
摘要：Finite-dimensional linear programs satisfy strong duality (SD) and have the dual pricing (DP) property. The DP property ensures that, given a sufficiently small perturbation of the right-hand-side vector, there exists a dual solution that correctly prices the perturbation by computing the exact change in the optimal objective function value. These properties may fail in semi-infinite linear programming where the constraint vector space is infinite dimensional. Unlike the finite-dimensional cas...
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作者：Charitha, C.; Dutta, Joydeep; Luke, D. Russell
作者单位：University of Gottingen; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; University of Gottingen
摘要：We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link in the relationship between the solution sets to these various regularized problems is the idea of exact regularization, which, in turn, is fundamentally associated with the existence of Lagrange multipliers for the regularized variational inequality. A regul...
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作者：Sun, Hailin; Su, Che-Lin; Chen, Xiaojun
作者单位：Nanjing University of Science & Technology; University of Chicago; Hong Kong Polytechnic University
摘要：Utility-based choice models are often used to determine a consumer's purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers' preferences over observed product characteristics. These models also serve as a building block in modeling firms' pricing and assortment optimization problems. We consider a firm's multiproduct pricing problem, in which product demands are det...
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作者：Yousefian, Farzad; Nedic, Angelia; Shanbhag, Uday V.
作者单位：Oklahoma State University System; Oklahoma State University - Stillwater; Arizona State University; Arizona State University-Tempe; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Traditionally, most stochastic approximation (SA) schemes for stochastic variational inequality (SVI) problems have required the underlying mapping to be either strongly monotone or monotone and Lipschitz continuous. In contrast, we consider SVIs with merely monotone and non-Lipschitzian maps. We develop a regularized smoothed SA (RSSA) scheme wherein the stepsize, smoothing, and regularization parameters are reduced after every iteration at a prescribed rate. Under suitable assumptions on the...
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作者：Rudloff, Birgit; Ulus, Firdevs; Vanderbei, Robert
作者单位：Vienna University of Economics & Business; Ihsan Dogramaci Bilkent University; Princeton University
摘要：In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans-Steuer) algorithm (Math Program 5(1):54-72, 1973). Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lohne (Vector optimization with infimum and supremum. Springer, Berlin, ...
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作者：de Carli Silva, Marcel K.; Tuncel, Levent
作者单位：Universidade de Sao Paulo; University of Waterloo
摘要：Lovasz theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the...
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作者：Yu, Jiajin; Ahmed, Shabbir
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: where N is a positive integer, is a concave function, are nonnegative vectors, d is a real number and B is a positive real number. We propose a family of inequalities for the convex hull of P by exploiting submodularity of the function over and the knapsack constraint . Computational effectiveness of the proposed inequalities within a branch-and-cut framework i...
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作者：Natarajan, Karthik; Teo, Chung-Piaw
作者单位：Singapore University of Technology & Design; National University of Singapore
摘要：We show that the complexity of computing the second order moment bound on the expected optimal value of a mixed integer linear program with a random objective coefficient vector is closely related to the complexity of characterizing the convex hull of the points where is the feasible region. In fact, we can replace the completely positive programming formulation for the moment bound on , with an associated semidefinite program, provided we have a linear or a semidefinite representation of this...
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作者：Facchinei, Francisco; Lampariello, Lorenzo; Scutari, Gesualdo
作者单位：Sapienza University Rome; Roma Tre University; Purdue University System; Purdue University
摘要：We propose a general feasible method for nonsmooth, nonconvex constrained optimization problems. The algorithm is based on the (inexact) solution of a sequence of strongly convex optimization subproblems, followed by a step-size procedure. Key features of the scheme are: (i) it preserves feasibility of the iterates for nonconvex problems with nonconvex constraints, (ii) it can handle nonsmooth problems, and (iii) it naturally leads to parallel/distributed implementations. We illustrate the app...
