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作者：Pflug, Georg Ch.
作者单位：University of Vienna
摘要：Measures of risk appear in two categories: Risk capital measures serve to determine the necessary amount of risk capital in order to avoid ruin if the outcomes of an economic activity are uncertain and their negative values may be interpreted as acceptability measures (safety measures). Pure risk measures (risk deviation measures) are natural generalizations of the standard deviation. While pure risk measures are typically convex, acceptability measures are typically concave. In both cases, th...
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作者：Jansen, K
作者单位：University of Kiel
摘要：We propose an approximation algorithm for, the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. The algorithm is based on a Lagrangian decomposition method and it uses a c-approximation algorithm (called approximate block solver) for a simpler maximization problem over the convex set B. We show that our algorithm achieves within O( M(1nM + is an element of(-2) 1n is an element of(-1))) iterations or calls to the approximate block solver a solut...
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作者：Wachter, A; Biegler, LT
作者单位：International Business Machines (IBM); IBM USA; Carnegie Mellon University
摘要：We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IP...
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作者：Fortz, B; Mahjoub, AR; McCormick, ST; Pesneau, P
作者单位：Universite Catholique Louvain; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); University of British Columbia
摘要：We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a ring) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together with the so-called cut inequalities yield an integer programming formulation of the problem in the space of the natural design variables. We then study the po...
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作者：Frangioni, A; Gentile, C
作者单位：University of Pisa; Consiglio Nazionale delle Ricerche (CNR); Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti (IASI-CNR)
摘要：We show that the convex envelope of the objective function of Mixed-Integer Programming problems with a specific structure is the perspective function of the continuous part of the objective function. Using a characterization of the subdifferential of the perspective function, we derive perspective cuts, a family of valid inequalities for the problem. Perspective cuts can be shown to belong to the general family of disjunctive cuts, but they do not require the solution of a potentially costly ...
