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作者：Attouch, Hedy; Bolte, Jerome; Svaiter, Benar Fux
作者单位：Universite de Montpellier; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Aojasiewicz inequality. This assumption allows to cover a wide range of problems, including nonsmooth semi-algebraic (or more generally tame) minimization. The spec...
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作者：Buchheim, Christoph; Wiegele, Angelika
作者单位：Dortmund University of Technology; University of Klagenfurt
摘要：We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for medium-sized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as a bounding routine in an SDP-based branch-and-bound framework. In case of a conv...
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作者：Zhao, Ming; de Farias, Ismael Regis, Jr.
作者单位：Texas Tech University System; Texas Tech University
摘要：We give new facets and valid inequalities for the separable piecewise linear optimization (SPLO) knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. Finally, we give computational results that demonstrate their efficiency in solving difficult instances of SPLO and SPLO with semi-continuous constraints.
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作者：Van Ngai Huynh; Huu Tron Nguyen; Thera, Michel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Limoges
摘要：In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.
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作者：Zymler, Steve; Kuhn, Daniel; Rustem, Berc
作者单位：Imperial College London
摘要：We develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove that this approximation is exact for robust individual chance constraints with concave or (n...
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作者：Duer, Mirjam; Hiriart-Urruty, Jean-Baptiste
作者单位：Universitat Trier; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the problem of minimizing an indefinite quadratic form over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective critical points and minima. We then apply a subgradient algorithm to approximate those critical points and obtain an efficient heuristic to verify n...
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作者：Mazade, Marc; Thibault, Lionel
作者单位：Universite de Montpellier
摘要：This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as -prox-regularity.
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作者：Wogrin, S.; Hobbs, B. F.; Ralph, D.; Centeno, E.; Barquin, J.
作者单位：Comillas Pontifical University; Johns Hopkins University; Johns Hopkins University; University of Cambridge; University of Cambridge
摘要：We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equi...
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作者：Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
作者单位：University of British Columbia
摘要：We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically regular firmly nonexpansive mappings is also asymptotically regular. Throughout, examples are provided...
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作者：Nie, Jiawang
作者单位：University of California System; University of California San Diego
摘要：Given polynomials f(x), g (i) (x), h(j)(x), we study how to minimize f(x) on the set S = {x is an element of R-n : h(1)(x) = ... = h(m1)(x) = 0, g(1)(x) >= 0, ... , g(m2)(x) >= 0}. Let f(min) be the minimum of f on S. Suppose S is nonsingular and f(min) is achievable on S, which are true generically. This paper proposes a new type semidefinite programming (SDP) relaxation which is the first one for solving this problem exactly. First, we construct new polynomials phi(1), ... , phi(r), by using...
