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作者：McCormick, S. Thomas; Fujishige, Satoru
作者单位：University of British Columbia; Kyoto University
摘要：Bisubmodular functions are a natural directed, or signed, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial vers...
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作者：Birgin, E. G.; Floudas, C. A.; Martinez, J. M.
作者单位：Universidade de Sao Paulo; Princeton University; Universidade Estadual de Campinas
摘要：A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.
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作者：Dentcheva, Darinka; Ruszczynski, Andrzej
作者单位：Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
摘要：We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconve...
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作者：Dutta, Joydeep; Pattanaik, Suvendu Ranjan; Thera, Michel
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
摘要：In this note we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the approximate multiplier rule.
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作者：Iwata, Satoru; Takamatsu, Mizuyo
作者单位：University of Tokyo; Kyoto University
摘要：Modern modeling approaches for circuit analysis lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The index of the DAE arising from the modified nodal analysis (MNA) is determined uniquely by the structure of the circuit. Instead, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant electric circuit...
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作者：Fernandez, Damian; Solodov, Mikhail
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the strong second-order sufficient condition for optimality (without any constraint qualification assumptions). We prove a stronger superlinear converge...
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作者：Dontchev, A. L.; Rockafellar, R. T.
作者单位：National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS); NSF - Division of Mathematical Sciences (DMS); University of Washington; University of Washington Seattle
摘要：In an extension of Newton's method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set of all associated sequences of Newton's iterates as elements of a sequence space. An inverse function version of this result shows that the strong regularity of the mapping associated with the Newton sequences is equivalent to the strong regularity of the generalized equation m...
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作者：Liu, Xinwei; Yuan, Yaxiang
作者单位：Hebei University of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a range-space step and a null-space step in every iteration. The a(2) penalty function is taken as the merit function. Under very mild conditions on range-space steps and approximate Hessians, without assuming any regularity, it is proved t...
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作者：Haddad, Tahar; Thibault, Lionel
作者单位：Universite de Montpellier; Universite de Jijel
摘要：In this paper we prove a theorem on the existence of a global solution of a differential inclusion governed by a class of nonconvex sweeping processes with unbounded pertubations. The perturbations are not required to be convex valued.
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作者：Pochet, Yves; Wolsey, Laurence A.
作者单位：Universite Catholique Louvain; Universite Catholique Louvain; Universite Catholique Louvain
摘要：We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is (i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs) and (ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially solvable using dynamic programming. When the capacities are non-decreasing, we derive a compact mixed integer programm...
