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作者：Combettes, Patrick L.; Eckstein, Jonathan
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allo...
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作者：Marandi, Ahmadreza; den Hertog, Dick
作者单位：Tilburg University
摘要：Adjustable robust optimization (ARO) generally produces better worst-case solutions than static robust optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we provide conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that when the uncertainty is constraint-wise, the problem is convex with respect to the adjustable variables and concave with respect to the uncertain parameters, the adjustable variables lie in a...
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作者：Yang, Boshi; Anstreicher, Kurt; Burer, Samuel
作者单位：Clemson University; University of Iowa
摘要：Let be a quadratically constrained, possibly nonconvex, bounded set, and let denote ellipsoids contained in with non-intersecting interiors. We prove that minimizing an arbitrary quadratic over is no more difficult than minimizing over in the following sense: if a given semidefinite-programming (SDP) relaxation for is tight, then the addition of l linear constraints derived from yields a tight SDP relaxation for . We also prove that the convex hull of equals the intersection of the convex hull...
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作者：Lee, Jae Hyoung; Lee, Gue Myung
作者单位：Pukyong National University
摘要：In this paper, we establish tractable sum of squares characterizations of the containment of a convex set, defined by a SOS-concave matrix inequality, in a non-convex set, defined by difference of a SOS-convex polynomial and a support function, with Slater's condition. Using our set containment characterization, we derive a zero duality gap result for a DC optimization problem with a SOS-convex polynomial and a support function, its sum of squares polynomial relaxation dual problem, the semide...
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作者：Kruger, A. Y.; Lopez, M. A.; Thera, M. A.
作者单位：Federation University Australia; Universitat d'Alacant; Centre National de la Recherche Scientifique (CNRS); Universite de Limoges
摘要：Our aim in the current article is to extend the developments in Kruger et al. (SIAM J Optim 20(6):3280-3296, 2010. doi:10.1137/100782206) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by lower semicontinuous functions under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn o...
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作者：Eghbahi, Reza; Saunderson, James; Fazel, Maryam
作者单位：Cisco Systems Inc; Cisco USA; Monash University; University of Washington; University of Washington Seattle
摘要：We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint. The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step. Of particular interest are classic experiment design problems in the online setting, with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially. We ana...
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作者：Xu, Huifu; Liu, Yongchao; Sun, Hailin
作者单位：University of Southampton; Dalian University of Technology; Nanjing University of Science & Technology
摘要：A key step in solving minimax distributionally robust optimization (DRO) problems is to reformulate the inner maximization w.r.t. probability measure as a semiinfinite programming problem through Lagrange dual. Slater type conditions have been widely used for strong duality (zero dual gap) when the ambiguity set is defined through moments. In this paper, we investigate effective ways for verifying the Slater type conditions and introduce other conditions which are based on lower semicontinuity...
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作者：Lee, Jon; Skipper, Daphne; Speakman, Emily
作者单位：University of Michigan System; University of Michigan; United States Department of Defense; United States Navy; United States Naval Academy; Otto von Guericke University
摘要：This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically comparing relaxations in the context of mixed-integer linear and nonlinear optimization, with the goal of gaining algorithmic and modeling insights. We consider relaxations of: fixed-charge formulations, vertex packing polytopes, boolean-quadric polytopes, and relaxations of graphs of monomials on box domains. Besides surveying the area...
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作者：Hoai An Le Thi; Tao Pham Dinh
作者单位：Universite de Lorraine
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作者：Adly, Samir; Dontchev, Asen
作者单位：Universite de Limoges; University of Michigan System; University of Michigan
