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作者：Ioffe, A; Lucchetti, RE
作者单位：Technion Israel Institute of Technology; Polytechnic University of Milan
摘要：In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and right-hand side perturbation of the constraints, while the core'' cost function and the left-hand side constraint functions are kept fixed. The main result shows that the set of the problems which are not well-posed is sigma-porous in a certain strong sense. Our results concern bot...
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作者：Harrington, JE; Hobbs, BF; Pang, JS; Liu, A; Roch, G
作者单位：Johns Hopkins University; Johns Hopkins University; Rensselaer Polytechnic Institute; Johns Hopkins University
摘要：A Nash-based collusive game among a finite set of players is one in which the players coordinate in order for each to gain higher payoffs than those prescribed by the Nash equilibrium solution. In this paper, we study the optimization problem of such a collusive game in which the players collectively maximize the Nash bargaining objective subject to a set of incentive compatibility constraints. We present a smooth reformulation of this optimization problem in terms of a nonlinear complementari...
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作者：Edmond, JF; Thibault, L
作者单位：Universite de Montpellier
摘要：We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes.
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作者：Cánovas, MJ; Dontchev, L; López, MA; Parra, J
作者单位：Universidad Miguel Hernandez de Elche; Universitat d'Alacant
摘要：We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F+g is not metrically regular is equal to the reciprocal to the modulus of regularity of F. The Lyusternik-Graves theorem gives a straightfo...
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作者：van Ngai, H; Théra, M
作者单位：Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
摘要：The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang & Pa...
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作者：Yao, XD; Zhou, JX
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：This paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design. Most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems. Thus they are not helpful for numerical algorithm design. Inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in [14, 15, 19, 21, 23], a local minimax characterization f...
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作者：Iusem, A; Seeger, A
作者单位：Avignon Universite
摘要：In this paper we explore the concept of antipodality relative to a closed convex cone K subset of R-d. The problem under consideration is that of finding a pair of unit vectors in K achieving the maximal angle of the cone. We mention also a few words on the attainability of critical angles. By way of application of the general theory, we briefly discuss the problem of estimating the radius of pointedness of a cone.
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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).
