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作者：Saxena, Anureet; Goyal, Vineet; Lejeune, Miguel A.
作者单位：Drexel University; Carnegie Mellon University
摘要：In this paper, we address the following probabilistic version (PSC) of the set covering problem: min{cx vertical bar P(Ax >= xi) >= p, x is an element of {0, 1}(N)} where A is a 0-1 matrix, xi is a random 0-1 vector and p is an element of (0, 1] is the threshold probability level. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at deriving an equivalent MIP reformulation of (PSC), the latter is used as a strengthening device to obtain a stronger formula...
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作者：Gould, N. I. M.; Toint, Ph. L.
作者单位：University of Namur; University of Oxford
摘要：A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate...
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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：Gutierrez, C.; Jimenez, B.; Novo, V.
作者单位：Universidad Nacional de Educacion a Distancia (UNED); Universidad de Valladolid
摘要：We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Fr,chet differentiable and their Fr,chet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our s...
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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：Anitescu, Mihai; Park, Sanghyun
作者单位：United States Department of Energy (DOE); Argonne National Laboratory
摘要：This work addresses the computation of free-energy differences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morphing procedure, we employ permutations of atoms: we seek to find the permutation sigma that minimizes the mean-square distance traveled by the atoms. Instead of performing this combinatorial search in the space of permutations, we show that the best permutation can be found by solving a line...
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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：Berstein, Y.; Lee, J.; Onn, S.; Weismantel, R.
作者单位：International Business Machines (IBM); IBM USA; Technion Israel Institute of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We address optimization of parametric nonlinear functions of the form f(Wx), where f : R-d -> R is a nonlinear function, W is a d x n matrix, and feasible x are in some large finite set F of integer points in R-n. Generally, such problems are intractable, so we obtain positive algorithmic results by looking at broad natural classes of f, W and F. One of our main motivations is multi-objective discrete optimization, where f trades off the linear functions given by the rows of W. Another motivat...
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作者：Helton, J. William; Nie, Jiawang
作者单位：University of California System; University of California San Diego
摘要：Let S = {x is an element of R-n : g(1)(x) >= 0, ..., g(m)(x) >= 0} be a semialgebraic set defined by multivariate polynomials g(i) (x). Assume S is convex, compact and has nonempty interior. Let S-i = {x is an element of R-n : g(i)(x) >= 0}, and partial derivative S (resp. partial derivative S-i ) be the boundary of S (resp. S-i ). This paper, as does the subject of semidefinite programming (SDP), concerns linear matrix inequalities (LMIs). The set S is said to have an LMI representation if it...
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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...
