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作者：Kojima, M; Kim, S; Waki, H
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology; Ewha Womans University
摘要：Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming (SDP) relaxation of polynomial optimization problems. We discuss effective methods to obtain a simpler representation of a sparse polynomial as a sum of squares of sparse polynomials by eliminating redundancy.
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作者：Mordukhovich, BS; Nam, NM
作者单位：Wayne State University
摘要：The paper is devoted to studying generalized differential properties of distance functions that play a remarkable role in variational analysis, optimization, and their applications. The main object under consideration is the distance function of two variables in Banach spaces that signifies the distance from a point to a moving set. We derive various relationships between Frechet-type subgradients and limiting (basic and singular) subgradients of this distance function and corresponding genera...
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作者：Henrion, R; Outrata, JV
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：The paper is devoted to the analysis of the calmness property for constraint set mappings. After some general characterizations, specific results are obtained for various types of constraints, e.g., one single nonsmooth inequality, differentiable constraints modeled by polyhedral sets, finitely and infinitely many differentiable inequalities. The obtained conditions enable the detection of calmness in a number of situations, where the standard criteria (via polyhedrality or the Aubin property)...
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作者：Jourani, A; Ye, JJ
作者单位：University of Victoria
摘要：In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefiniteness (such as in semidefinite programming).
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作者：Çezik, MT; Iyengar, G
作者单位：Universite de Montreal; Universite de Montreal; Columbia University
摘要：In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomor...
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作者：Meng, FW; Sun, DF; Zhao, GY
作者单位：University of Southampton; National University of Singapore
摘要：We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the ...
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作者：Qi, LQ; Shapiro, A; Ling, C
作者单位：Hong Kong Polytechnic University; University System of Georgia; Georgia Institute of Technology; Zhejiang University of Finance & Economics
摘要：In this paper we study differentiability and semismoothness properties of functions defined as integrals of parameterized functions. We also discuss applications of the developed theory to the problems of shape-preserving interpolation, option pricing and semi-infinite programming.
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作者：Danna, E; Rothberg, E; Le Pape, C
作者单位：Centre National de la Recherche Scientifique (CNRS); Avignon Universite
摘要：Given a feasible solution to a Mixed Integer Programming (MIP) model, a natural question is whether that solution can be improved using local search techniques. Local search has been applied very successfully in a variety of other combinatorial optimization domains. Unfortunately, local search relies extensively on the notion of a solution neighborhood, and this neighborhood is almost always tailored to the structure of the particular problem being solved. A MIP model typically conveys little ...
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作者：Burachik, RS; Jeyakumar, V
作者单位：Universidade Federal do Rio de Janeiro; University of New South Wales Sydney
摘要：In 1951, Fenchel discovered a special duality, which relates the minimization of a sum of two convex functions with the maximization of the sum of concave functions, using conjugates. Fenchel's duality is central to the study of constrained optimization. It requires an existence of an interior point of a convex set which often has empty interior in optimization applications. The well known relaxations of this requirement in the literature are again weaker forms of the interior point condition....
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作者：Berkelaar, A; Gromicho, JAS; Kouwenberg, R; Zhang, SZ
作者单位：Vrije Universiteit Amsterdam; Chinese University of Hong Kong
摘要：This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their o...
