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作者：Eichfelder, Gabriele
作者单位：University of Erlangen Nuremberg
摘要：In this work nonlinear non-convex multiobjective bilevel optimization problems are discussed using an optimistic approach. It is shown that the set of feasible points of the upper level function, the so-called induced set, can be expressed as the set of minimal solutions of a multiobjective optimization problem. This artificial problem is solved by using a scalarization approach by Pascoletti and Serafini combined with an adaptive parameter control based on sensitivity results for this problem...
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作者：Gritzmann, Peter; Ritter, Michael; Zuber, Paul
作者单位：Technical University of Munich; Technical University of Munich
摘要：A key issue for high integration circuit design in the semiconductor industry are power constraints that stem from the need for heat removal and reliability or battery lifetime limitations. As the power consumption depends heavily on the capacitances between adjacent wires, determining the optimal ordering and spacing of parallel wires is an important issue in the design of low power chips. As it turns out, optimal wire spacing is a convex optimization problem, whereas the optimal wire orderin...
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作者：Bao, Truong Q.; Mordukhovich, Boris S.
作者单位：Wayne State University
摘要：In this paper we introduce and study enhanced notions of relative Pareto minimizers for constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers for general multiobjective problems under a refined...
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作者：Schlenkrich, Sebastian; Griewank, Andreas; Walther, Andrea
作者单位：Technische Universitat Dresden; Humboldt University of Berlin
摘要：The numerical solution of nonlinear equation systems is often achieved by so-called quasi-Newton methods. They preserve the rapid local convergence of Newton's method at a significantly reduced cost per step by successively approximating the system Jacobian though low-rank updates. We analyze two variants of the recently proposed adjoint Broyden update, which for the first time combines the classical least change property with heredity on affine systems. However, the new update does require, t...
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作者：Yuan, Ya-xiang
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This short note gives the sharp bound for the Q-linear convergence rate of the iterates generated by the steepest descent method with exact line searches when the objective function is strictly convex quadratic.
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作者：Elhallaoui, Issmail; Metrane, Abdelmoutalib; Soumis, Francois; Desaulniers, Guy
作者单位：Universite de Montreal; Polytechnique Montreal; Universite de Montreal
摘要：Dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems. This speed up is mostly due to the use, at each iteration, of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model. This aggregation is updated when needed to ensure the exactness of the overall approach. In this paper, we propose a new version of this method, called the m...
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作者：Rendl, Franz; Rinaldi, Giovanni; Wiegele, Angelika
作者单位：University of Klagenfurt; Consiglio Nazionale delle Ricerche (CNR); Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti (IASI-CNR)
摘要：We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a nearly optimal solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-C...
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作者：Pang, Jong-Shi
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonl...
