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作者：Houska, Boris; Diehl, Moritz
作者单位：KU Leuven
摘要：In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min-max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curv...
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作者：Geihe, Benedict; Lenz, Martin; Rumpf, Martin; Schultz, Ruediger
作者单位：University of Bonn; University of Duisburg Essen
摘要：Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a regular lattice. Here, in a two dimensional set up we focus on ellipsoidal holes as the fine scale geometric details described by the semiaxes and their orientation. Optimization of a deterministic cost functional as well as stochastic loading with risk neutral and risk averse stochastic cost functionals...
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作者：Aussel, D.; Eberhard, A.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Perpignan Via Domitia; Royal Melbourne Institute of Technology (RMIT)
摘要：The concept of maximal quasimonotonicity of set-valued map is introduced and studied. Regularity properties of this class of operators is investigated, in particular the ccvc property, an adaptation to the quasimonotone case of the classical notion of cusco map. In an Asplund space, we provide sufficient conditions for a ccvc quasimonotone operator to be single-directional on a -dense subset.
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作者：Li, Guoyin
作者单位：University of New South Wales Sydney
摘要：In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Holder-type global error bound with an explicit Holder exponent. Our result extends the corresponding results of Li (SIAM J Control Optim 33(5):1510-1529, 1995) from piecewise convex quadratic functions to piecewise convex polynomials.
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作者：Dontchev, A. L.; Rockafellar, R. T.
作者单位：University of Washington; University of Washington Seattle
摘要：For solving the generalized equation , where is a smooth function and is a set-valued mapping acting between Banach spaces, we study the inexact Newton method described by (f(x(k)) + Df(x(k))(x(k+1) - x(k)) + F(x(k+1) )) boolean AND R-k(x(k), x(k+1) ) not equal empty set, where is the derivative of and the sequence of mappings represents the inexactness. We show how regularity properties of the mappings and are able to guarantee that every sequence generated by the method is convergent either ...
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作者：Hemmecke, Raymond; Onn, Shmuel; Romanchuk, Lyubov
作者单位：Technical University of Munich; Technion Israel Institute of Technology
摘要：n-Fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for n-fold integer programming predating the present article runs in time with L the binary length of the numerical part of the input and g(A) the so-called Graver complexity of the bimatrix A defining the system. In this article we ...
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作者：Tawarmalani, Mohit; Richard, Jean-Philippe P.; Xiong, Chuanhui
作者单位：Purdue University System; Purdue University; State University System of Florida; University of Florida; University of North Carolina; University of North Carolina at Pembroke
摘要：In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.
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作者：Van Vyve, Mathieu
摘要：In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying bipartite graph. We further motivate its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem, and a generalization of a simple variant of the single-node flow set. This paper is essentially a polyhedral analysis ...
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作者：Amaral, Andre R. S.; Letchford, Adam N.
作者单位：Universidade Federal do Espirito Santo; Lancaster University
摘要：The single row facility layout problem (SRFLP) is the NP-hard problem of arranging facilities on a line, while minimizing a weighted sum of the distances between facility pairs. In this paper, a detailed polyhedral study of the SRFLP is performed, and several huge classes of valid and facet-inducing inequalities are derived. Some separation heuristics are presented, along with a primal heuristic based on multi-dimensional scaling. Finally, a branch-and-cut algorithm is described and some encou...
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作者：Pecher, Arnaud; Wagler, Annegret K.
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Universite Clermont Auvergne (UCA)
摘要：A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Grotschel et al. in Combinatorica 1(2):169-197, 1981). Perfect graphs have the key property that clique and chromatic number coincide for all induced subgraphs; we address the question whether the algorithmic results for perfect graphs can be extended to graph classes where the chromatic number of all members is bounded by the clique number plus one. We consider...
