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作者：Zheng, XY; Ng, KF
作者单位：Yunnan University; Chinese University of Hong Kong
摘要：Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat's rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke's normal cones or the limiting normal cones) for Pareto efficient points.
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作者：Gilbert, JC; Gonzaga, CC; Karas, E
作者单位：Universidade Federal de Santa Catarina (UFSC); Universidade Federal do Parana
摘要：This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.
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作者：Stork, F; Uetz, M
作者单位：Maastricht University; Technical University of Berlin
摘要：We present several complexity results related to generation and counting of all circuits of an independence system. Our motivation to study these problems is their relevance in the solution of resource constrained scheduling problems, where an independence system arises as the subsets of jobs that may be scheduled simultaneously. We are interested in the circuits of this system, the so-called minimal forbidden sets, which are minimal subsets of jobs that must not be scheduled simultaneously. A...
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作者：Zhao, GY
作者单位：National University of Singapore
摘要：This paper presents an algorithm for solving multi-stage stochastic convex nonlinear programs. The algorithm is based on the Lagrangian dual method which relaxes the nonanticipativity constraints, and the barrier function method which enhances the smoothness of the dual objective function so that the Newton search directions can be used. The algorithm is shown to be of global convergence and of polynomial-time complexity.
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作者：Goldfarb, D; Scheinberg, K
作者单位：Columbia University; International Business Machines (IBM); IBM USA
摘要：Second-order cone programming (SOCP) problems are typically solved by interior point methods. As in linear programming (LP), interior point methods can, in theory, solve SOCPs in polynomial time and can, in practice, exploit sparsity in the problem data. Specifically, when cones of large dimension are present, the density that results in the normal equations that are solved at each iteration can be remedied in a manner similar to the treatment of dense columns in an LP. Here we propose a produ...
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作者：Lin, JG
摘要：This paper examines Pareto optimality of solutions to multi-objective problems scalarized in the min-norm, compromise programming, generalized goal programming, or unrestricted min-max formulations. Issues addressed include, among others, uniqueness in solution or objective space, penalization for overachievement of goals, min-max reformulation of goal programming, inferiority in Tchebycheff-nonn minimization, strength and weakness of weighted-bound optimization, quasi-satisficing decision-mak...
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作者：Yamashita, H; Yabe, H; Tanabe, T
作者单位：Tokyo University of Science
摘要：This paper proposes a primal-dual interior point method for solving large scale nonlinearly constrained optimization problems. To solve large scale problems, we use a trust region method that uses second derivatives of functions for minimizing the barrier-penalty function instead of line search strategies. Global convergence of the proposed method is proved under suitable assumptions. By carefully controlling parameters in the algorithm, superlinear convergence of the iteration is also proved....
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作者：Sen, S; Higle, JL
作者单位：University of Arizona
摘要：This paper considers the two-stage stochastic integer programming problem, with an emphasis on instances in which integer variables appear in the second stage. Drawing heavily on the theory of disjunctive programming, we characterize convexifications of the second stage problem and develop a decomposition-based algorithm for the solution of such problems. In particular, we verify that problems with fixed recourse are characterized by scenario-dependent second stage convexifications that have a...
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作者：Zhao, L; Nagamochi, H; Ibaraki, T
作者单位：Utsunomiya University; Toyohashi University of Technology; Kyoto University
摘要：Given a system (V, T, f, k), where V is a finite set, T subset of or equal to V, f : 2(V) --> R is a submodular function and k greater than or equal to 2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition P = {V-1, V-2,..., V-k} of V that satisfies V-i boolean AND T not equal empty set for all i and minimizes f (V-1) + f (V-2)+...+ f (V-k), where P is a k-partition of V if ( i) V-i not equal empty set, (ii) V-i boolean AND V-j = empty set, i not equal j, and...
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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.
