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作者：Powell, M. J. D.
作者单位：University of Cambridge
摘要：Some highly successful algorithms for unconstrained minimization without derivatives construct changes to the variables by applying trust region methods to quadratic approximations to the objective function . A quadratic model has (n + 1) (n + 2)/2 independent parameters, but each new model may interpolate only 2n + 1 values of F, for instance. The symmetric Broyden method takes up the remaining freedom by minimizing the Frobenius norm of the difference between the second derivative matrices o...
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作者：Chen, Xiaojun; Xiang, Shuhuang
作者单位：Hong Kong Polytechnic University; Central South University
摘要：We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in the differential equation. Moreover, we present a simple formula to compute an element in the Clarke...
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作者：Kong, Nan; Schaefer, Andrew J.; Ahmed, Shabbir
作者单位：Purdue University System; Purdue University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University System of Georgia; Georgia Institute of Technology
摘要：We consider totally unimodular (TU) stochastic programs, that is, two-stage stochastic programs whose extensive-form constraint matrix is TU. We generalize the notion of total unimodularity to apply to sets of matrices and provide properties of such sets. We provide several sufficient conditions on stochastic programs to be TU. When solving TU stochastic problems using the L-shaped method, it is not clear whether the integrality restrictions should be imposed on the master problem. Such restri...
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作者：Fischer, Anja; Helmberg, Christoph
作者单位：Technische Universitat Chemnitz
摘要：In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a linearized integer programming formulation of the symmetric quadratic traveling salesman problem. Our constru...
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作者：Hildebrand, Roland
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Let K subset of R-n be a regular convex cone, let e(1), ... , e(n) is an element of partial derivative K be linearly independent points on the boundary of a compact affine section of the cone, and let x* is an element of K-0 be a point in the relative interior of this section. For k = 1, ... , n, let l(k) be the line through the points e(k) and x*, let y(k) be the intersection point of l(k) with partial derivative K opposite to e(k), and let z(k) be the intersection point of l(k) with the line...
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作者：Schiro, Dane A.; Pang, Jong-Shi; Shanbhag, Uday V.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Affine generalized Nash equilibrium problems (AGNEPs) represent a class of non-cooperative games in which players solve convex quadratic programs with a set of (linear) constraints that couple the players' variables. The generalized Nash equilibria (GNE) associated with such games are given by solutions to a linear complementarity problem (LCP). This paper treats a large subclass of AGNEPs wherein the coupled constraints are shared by, i.e., common to, the players. Specifically, we present sev...
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作者：Simonetti, Luidi; da Cunha, Alexandre Salles; Lucena, Abilio
作者单位：Universidade Federal Fluminense; Universidade Federal de Minas Gerais; Universidade Federal do Rio de Janeiro
摘要：Given an undirected graph G with vertex and edge weights, the k-cardinality tree problem asks for a minimum weight tree of G containing exactly k edges. In this paper we consider a directed graph reformulation of the problem and carry out a polyhedral investigation of the polytope defined by the convex hull of its feasible integral solutions. Three new families of valid inequalities are identified and two of them are proven to be facet implying for that polytope. Additionally, a Branch-and-cut...
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作者：Robinson, Stephen M.
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：This paper studies the local analysis of equations on a product U x U of Banach spaces, whose variables lie in a subset having the special property that it is locally Lipschitz-homeomorphic to an open subset of U. A prominent example, to which we devote most of the paper, is a system of equations whose variables lie in the graph of a maximal monotone operator. This general formulation covers many specific problems of interest, and our objective is to understand the local behavior of solutions ...
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作者：Bouza Allende, Gemayqzel; Still, Georg
作者单位：Universidad de la Habana; University of Twente
摘要：Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach f...
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作者：Schiela, Anton
作者单位：Zuse Institute Berlin
摘要：We propose and analyze an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments.
