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作者：Lourenco, Bruno F.
作者单位：University of Tokyo
摘要：We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual functions. For amenable cones, it is shown that error bounds can be expressed as a composition of facial residual functions. The number of compositions is related to the facial reduction technique and the singularity degree of the problem. In particular, we show that...
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作者：Burer, Samuel; Ye, Yinyu
作者单位：University of Iowa; Stanford University
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作者：Lasserre, Jean B.; Weisser, Tillmann
作者单位：Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; United States Department of Energy (DOE); Los Alamos National Laboratory; United States Department of Energy (DOE); Los Alamos National Laboratory
摘要：Given X. Rn, e. (0, 1), a parametrized family of probability distributions (mu a)a.A on similar to. Rp, we consider the feasible set X* e. X associated with the distributionally robust chance-constraint X* e = {x. X : Prob mu[ f (x,.) > 0] > 1 - e,. mu. Ma}, whereMa is the set of all possibles mixtures of distributions mu a, a. A. For instance and typically, the family Ma is the set of all mixtures of Gaussian distributions on R with mean and standard deviation a = (a, s) in some compact set A...
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作者：Mordukhovich, Boris S.; Perez-Aros, Pedro
作者单位：Wayne State University; Universidad de O'Higgins
摘要：This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral r...
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作者：Ta, Thuy Anh; Mai, Tien; Bastin, Fabian; L'Ecuyer, Pierre
作者单位：Singapore-MIT Alliance for Research & Technology Centre (SMART); Universite de Montreal; Universite de Montreal
摘要：We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study asample average approximation(SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate the next-stage constraints. This approach provides an approximate solution to the multistage p...
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作者：Boehnlein, Toni; Kratsch, Stefan; Schaudt, Oliver
作者单位：University of Cologne; University of Bonn; RWTH Aachen University
摘要：In a Stackelberg Pricing Game a distinguished player, the leader, chooses prices for a set of items, and the other players, the followers, each seek to buy a minimum cost feasible subset of the items. The goal of the leader is to maximize her revenue, which is determined by the sold items and their prices. Most previously studied cases of such games can be captured by a combinatorial model where we have a base set of items, some with fixed prices, some priceable, and constraints on the subsets...
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作者：Gnegel, Fabian; Fuegenschuh, Armin; Hagel, Michael; Leyffer, Sven; Stiemer, Marcus
作者单位：Brandenburg University of Technology Cottbus; United States Department of Energy (DOE); Argonne National Laboratory
摘要：We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variab...
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作者：Ouyang, Yuyuan; Xu, Yangyang
作者单位：Clemson University; Rensselaer Polytechnic Institute
摘要：On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many iterations would guarantee a solution of desired accuracy. In this paper, we pursue the opposite direction by deriving lower complexity bounds of first-order methods on large-scale SPPs. Our results apply to the methods whose iterates are in the linear span of...
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作者：Perez-Aros, Pedro; Salas, David; Vilches, Emilio
作者单位：Universidad de O'Higgins; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：We show, in Hilbert space setting, that any two convex proper lower semicontinuous functions bounded from below, for which the norm of their minimal subgradients coincide, they coincide up to a constant. Moreover, under classic boundary conditions, we provide the same results when the functions are continuous and defined over an open convex domain. These results show that for convex functions bounded from below, the slopes provide sufficient first-order information to determine the function up...
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作者：Gomez, Andres
作者单位：University of Southern California
摘要：We study the convex hull of the mixed-integer set given by a conic quadratic inequality and indicator variables. Conic quadratic terms are often used to encode uncertainties, while the indicator variables are used to model fixed costs or enforce sparsity in the solutions. We provide the convex hull description of the set under consideration when the continuous variables are unbounded. We propose valid nonlinear inequalities for the bounded case, and show that they describe the convex hull for ...
