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作者：Kirlik, Gokhan; Sayin, Serpil
作者单位：Koc University
摘要：The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify a Decision Maker's most preferred solution without generating the entire set of nondominated solutions. We propose a bilevel programming formulation that can be used to this end. The bilevel program is capable of delivering an efficient solution that maps into a given set, provided that one exits. If the Decision Maker's prefe...
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作者：Zhang, Shuai; Xin, Jack
作者单位：University of California System; University of California Irvine
摘要：We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed (TL1), and its application in compressed sensing (CS). The TL1 penalty interpolates and norms through a nonnegative parameter , similar to with , and is known to satisfy unbiasedness, sparsity and Lipschitz continuity properties. We first consider the constrained minimization problem, and discuss the exact recovery of norm minimal solution based on the null space property (NSP). We then prove...
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作者：Burke, James V.; Eaton, Julia
作者单位：University of Washington; University of Washington Seattle; University of Washington; University of Washington Tacoma
摘要：The spectral abscissa is the largest real part of an eigenvalue of a matrix and the spectral radius is the largest modulus. Both are examples of spectral max functions-the maximum of a real-valued function over the spectrum of a matrix. These mappings arise in the control and stabilization of dynamical systems. In 2001, Burke and Overton characterized the regular subdifferential of the spectral abscissa and showed that the spectral abscissa is subdifferentially regular in the sense of Clarke w...
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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：Louveaux, Quentin; Skutella, Martin
作者单位：University of Liege; Technical University of Berlin
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作者：Singh, Mohit; Zenklusen, Rico
作者单位：Microsoft; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First results highlight several interesting advantages of k-trails compared to previous routing approaches. However, so far, only little is known regarding computational aspects of k-trails. In this work we aim to fill this gap by presenting how k-trails can be a...
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作者：Todd, Michael J.
作者单位：Cornell University
摘要：The max-k-sum of a set of real scalars is the maximum sum of a subset of size k, or alternatively the sum of the k largest elements. We study two extensions: first, we show how to obtain smooth approximations to functions that are pointwise max-k-sums of smooth functions. Second, we discuss how the max-k-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed convex cone.
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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...
