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• Optimized Bonferroni approximations of distributionally robust joint chance constraints AI翻译
  作者：Xie, Weijun; Ahmed, Shabbir; Jiang, Ruiwei
  作者单位：Virginia Polytechnic Institute & State University; University System of Georgia; Georgia Institute of Technology; University of Michigan System; University of Michigan
  摘要：A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold epsilon, over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to approximate the joint chance constraint by a system of single chance constraints, one for each original uncertain constrain...
• Quantitative stability analysis for minimax distributionally robust risk optimization AI翻译
  作者：Pichler, Alois; Xu, Huifu
  作者单位：Technische Universitat Chemnitz; University of Southampton
  摘要：This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage. We carry out a stability analysis by looking into variations of the ambiguity set under the Wasserstein metric, decision spaces at both stages and the support set of the random variables. In the case when the risk measure is risk neutral, the stability result is presented with the variation o...
• First-order inertial algorithms involving dry friction damping AI翻译
  作者：Adly, Samir; Attouch, Hedy
  作者单位：Universite de Limoges; Centre National de la Recherche Scientifique (CNRS); Universite de Montpellier
  摘要：In aHilbert spaceH, we introduce a newclass of first-order algorithms which naturally occur as discrete temporal versions of an inertial differential inclusion jointly involving viscous friction and dry friction. The function f : H -> Rto be minimized is supposed to be differentiable (not necessarily convex), and enters the algorithm via its gradient. The dry friction damping function phi : H -> R+ is convex with a sharp minimum at the origin, (typically phi(x) = r parallel to x parallel to wi...
• Subcontracting and lot-sizing with constant capacities AI翻译
  作者：Hwang, Hark-Chin
  作者单位：Kyung Hee University
  摘要：In this paper, we consider the subcontracting and single-item lot-sizing problem with constant capacities, which is uncapacitated in subcontracting but capacitated in production. For a holistic understanding of the problem, an infinite-period model is proposed. Such a model provides a unified view of a capacitated lot-sizing problem. The usefulness of the infinite-period model is shown by the principle that the firm's production schedule drives the subcontractor's supply schedule. For efficien...
• Nonlinear chance-constrained problems with applications to hydro scheduling AI翻译
  作者：Lodi, Andrea; Malaguti, Enrico; Nannicini, Giacomo; Thomopulos, Dimitri
  作者单位：Universite de Montreal; Polytechnique Montreal; University of Bologna; International Business Machines (IBM); IBM USA; University of Pisa
  摘要：We present a Branch-and-Cut algorithm for a class of nonlinear chance-constrained mathematical optimization problems with a finite number of scenarios. Unsatisfied scenarios can enter a recovery mode. This class corresponds to problems that can be reformulated as deterministic convex mixed-integer nonlinear programming problems with indicator variables and continuous scenario variables, but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows....
• Two-stage linear decision rules for multi-stage stochastic programming AI翻译
  作者：Bodur, Merve; Luedtke, James R.
  作者单位：University of Toronto; University of Wisconsin System; University of Wisconsin Madison
  摘要：Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed uncertain parameters. Finding an optimal LDR is a static optimization problem that provides an upper bound on the optimal value of the MSLP, and, under certain assumptions, can be formulated as an explicit linear program. Similarly, as proposed by Kuhn et al. (M...
• On standard quadratic programs with exact and inexact doubly nonnegative relaxations AI翻译
  作者：Gokmen, Y. Gorkem; Yildirim, E. Alper
  作者单位：Izmir Ekonomi Universitesi; University of Edinburgh
  摘要：The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices. Replacing the intractable cone in this formulation by the larger but tractable cone of doubly nonnegative matrices, i.e., the cone of positive semidefinite and componentwise nonnegative matrices, one obtains the so-called doubly nonnegative relaxation, whose ...
• Maximizing products of linear forms, and the permanent of positive semidefinite matrices AI翻译
  作者：Yuan, Chenyang; Parrilo, Pablo A.
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite (HPSD) matrices. By analyzing a constructive randomized rounding algorithm, we obtain an improved multiplicative approximation factor to the permanent of HPSD matrices, as well as computationally efficient certificates for this approximation. We also propose an...
• Problem-based optimal scenario generation and reduction in stochastic programming AI翻译
  作者：Henrion, R.; Roemisch, W.
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin
  摘要：Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear two-stage stochastic programs we show that the problem-based approach to optimal scenario generation can be reformulated as best appro...
• Role of sparsity and structure in the optimization landscape of non-convex matrix sensing AI翻译
  作者：Molybog, Igor; Sojoudi, Somayeh; Lavaei, Javad
  作者单位：University of California System; University of California Berkeley
  摘要：In this work, we study the optimization landscape of the non-convex matrix sensing problem that is known to have many local minima in the worst case. Since the existing results are related to the notion of restricted isometry property (RIP) that cannot directly capture the underlying structure of a given problem, they can hardly be applied to real-world problems where the amount of data is not exorbitantly high. To address this issue, we develop the notion of kernel structure property to obtai...