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作者：Bertsimas, Dimitris; Gupta, Vishal; Kallus, Nathan
作者单位：Massachusetts Institute of Technology (MIT); University of Southern California; Cornell University
摘要：The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems ...
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作者：Fan, Jinyan; Nie, Jiawang; Zhou, Anwa
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; University of California System; University of California San Diego; Shanghai University
摘要：This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial optimization. When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity. When no tensor is strictly copositive, we formulate the tensor eigenvalue complementarity ...
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作者：Fischer, Anja; Fischer, Frank; McCormick, S. Thomas
作者单位：University of Gottingen; Universitat Kassel; University of British Columbia
摘要：Recently, Buchheim and Klein (Discrete Appl Math 177:34-52, 2014) suggested to study polynomial-time solvable optimisation problems with linear objective functions combined with exactly one additional quadratic monomial. They concentrated on special quadratic spanning tree or forest problems. We extend their results to general matroid optimisation problems with a set of nested monomials in the objective function. We study polytopes arising from the standard linearisation of the monomials. Our ...
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作者：Mordukhovich, Boris S.; Sarabi, M. Ebrahim
作者单位：Wayne State University; Peoples Friendship University of Russia; University System of Ohio; Miami University
摘要：In this paper we introduce the notions of critical and noncritical multipliers for variational systems and extend to a general framework the corresponding notions by Izmailov and Solodov developed for classical Karush-Kuhn-Tucker (KKT) systems. It has been well recognized that critical multipliers are largely responsible for slow convergence of major primal-dual algorithms of optimization. The approach of this paper allows us to cover KKT systems arising in various classes of smooth and nonsmo...
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作者：Averkov, Gennadiy; Kaibel, Volker; Weltge, Stefan
作者单位：Otto von Guericke University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We relate the maximum semidefinite and linear extension complexity of a family of polytopes to the cardinality of this family and the minimum pairwise Hausdorff distance of its members. This result directly implies a known lower bound on the maximum semidefinite extension complexity of 0/1-polytopes. We further show how our result can be used to improve on the corresponding bounds known for polygons with integer vertices. Our geometric proof builds upon nothing else than a simple well-known pr...
