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作者：Canovas, M. J.; Hantoute, A.; Parra, J.; Toledo, F. J.
作者单位：Universidad Miguel Hernandez de Elche; Universidad de Chile
摘要：This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the framework of canonical perturbations (i.e., perturbations of the objective function and the right-hand-side of the constraints), the paper provides ...
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作者：Philpott, Andy; Ferris, Michael; Wets, Roger
作者单位：University of Auckland; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Davis
摘要：The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to single-period electricity pool auctions in which price-taking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In hydro-thermal markets where the auctions are repeated over many periods, agents seek to optimize their current and future profit accounting for fut...
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作者：Razaviyayn, Meisam; Sanjabi, Maziar; Luo, Zhi-Quan
作者单位：Stanford University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step, which can be expensive. In this paper, we propose a stochastic successive upper-bound minimization method (SSUM) which minimizes an approximate ensemble average at each iteration. To ensure convergence and to facilitate computation, we re...
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作者：Deng, Yan; Shen, Siqian
作者单位：University of Michigan System; University of Michigan
摘要：This paper investigates a problem of scheduling appointments with random service durations on multiple servers with operating time limits. We minimize the cost of operating servers and serving appointments, subject to a joint chance constraint limiting the risk of server running overtime. With finite samples of random service time, we consider a mixed-integer linear programming extended formulation and propose a two-stage decomposition framework with cutting planes. The first stage considers a...
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作者：Li, Xudong; Sun, Defeng; Toh, Kim-Chuan
作者单位：National University of Singapore; National University of Singapore
摘要：This paper is devoted to the design of an efficient and convergent semi-proximal alternating direction method of multipliers (ADMM) for finding a solution of low to medium accuracy to convex quadratic conic programming and related problems. For this class of problems, the convergent two block semi-proximal ADMM can be employed to solve their primal form in a straightforward way. However, it is known that it is more efficient to apply the directly extended multi-block semi-proximal ADMM, though...
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作者：Modaresi, Sina; Kilinc, Mustafa R.; Vielma, Juan Pablo
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Carnegie Mellon University; Massachusetts Institute of Technology (MIT)
摘要：We study the generalization of split, k-branch split, and intersection cuts from mixed integer linear programming to the realm of mixed integer nonlinear programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split, k-branch split, and intersection cuts for several classes of non-...
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作者：Shalev-Shwartz, Shai; Zhang, Tong
作者单位：Hebrew University of Jerusalem; Rutgers University System; Rutgers University New Brunswick; Baidu
摘要：We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve state-of-the-art results for various key machine learning optimization problems including SVM, logistic regression, ridge regression, Lasso, and multiclass SVM. Experiments validate our theoretical findings.
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作者：Shefi, Ron; Teboulle, Marc
作者单位：Tel Aviv University
摘要：We consider the class of nondifferentiable convex problems which minimizes a nonsmooth convex objective over a single smooth constraint. Exploiting the smoothness of the feasible set and using duality, we introduce a simple first order algorithm proven to globally converge to an optimal solution with a efficiency estimate. The performance of the algorithm is demonstrated by solving large instances of the convex sparse recovery problem.
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作者：Camlibel, M. K.; Schumacher, J. M.
作者单位：University of Groningen; Dogus University; Tilburg University
摘要：This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is passive and the static relation is maximal monotone. Based on the classical results on such differential inclusions, we conclude that such interconnections are well-posed in the sense of existence a...
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作者：Ahmed, Shabbir; Linderoth, Jeff
