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作者：Stewart, David E.
作者单位：University of Iowa
摘要：In this paper we consider the question of which matrices M give unique solutions for Differential Complementarity Problems (Mandelbaum 1989, unpublished manuscript) of the form dw/dt = Mz + q(t), w(0) = w(0) K ?? z(t) perpendicular to w(t) is an element of K* for all t, for all q and w(0) is an element of K* where K is a closed convex cone. Explicit descriptions of the set of such matrices are given for the 2 x 2 case; the set of such M's independent of K is a strict subset of the set of posit...
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作者：Cornuejols, Gerard; Margot, Francois
作者单位：Carnegie Mellon University; Aix-Marseille Universite
摘要：In this paper we consider an infinite relaxation of the mixed integer linear program with two integer variables, nonnegative continuous variables and two equality constraints, and we give a complete characterization of its facets. We also derive an analogous characterization of the facets of the underlying finite integer program.
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作者：Kim, Sunyoung; Kojima, Masakazu; Toint, Philippe
作者单位：Ewha Womans University; Institute of Science Tokyo; Tokyo Institute of Technology; University of Namur
摘要：Exploiting sparsity is essential to improve the efficiency of solving large optimization problems. We present a method for recognizing the underlying sparsity structure of a nonlinear partially separable problem, and show how the sparsity of the Hessian matrices of the problem's functions can be improved by performing a nonsingular linear transformation in the space corresponding to the vector of variables. A combinatorial optimization problem is then formulated to increase the number of zeros...
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作者：Belloni, Alexandre; Freund, Robert M.
作者单位：Massachusetts Institute of Technology (MIT); Duke University
摘要：In this paper we study the homogeneous conic system F : Ax = 0, is an element of C\{0}. We choose a point (s) over bar. is an element of intC* that serves as a normalizer and consider computational properties of the normalized system F (s) over bar : Ax = 0, s(-T) x = 1, x is an element of C. We show that the computational complexity of solving F via an interior-point method depends only on the complexity value v of the barrier for C and on the symmetry of the origin in the image set H ((s)) o...
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作者：Bonami, Pierre; Cornuejols, Gerard; Lodi, Andrea; Margot, Francois
作者单位：Carnegie Mellon University; Aix-Marseille Universite; University of Bologna
摘要：We present an algorithm for finding a feasible solution to a convex mixed integer nonlinear program. This algorithm, called Feasibility Pump, alternates between solving nonlinear programs and mixed integer linear programs. We also discuss how the algorithm can be iterated so as to improve the first solution it finds, as well as its integration within an outer approximation scheme. We report computational results.
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作者：Richard, Jean-Philippe P.; Li, Yanjun; Miller, Lisa A.
作者单位：Purdue University System; Purdue University; Purdue University System; Purdue University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we present an approximate lifting scheme to derive valid inequalities for general mixed integer programs and for the group problem. This scheme uses superadditive functions as the building block of integer and continuous lifting procedures. It yields a simple derivation of new and known families of cuts that correspond to extreme inequalities for group problems. This new approximate lifting approach is constructive and potentially efficient in computation.
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作者：Liu, C. G.; Ng, K. F.; Yang, W. H.
作者单位：Jinan University; Chinese University of Hong Kong; Fudan University
摘要：We study the weak domination property and weakly efficient solutions in vector optimization problems. In particular scalarization of these problems is obtained by virtue of some suitable merit functions. Some natural conditions to ensure the existence of error bounds for merit functions are also given.
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作者：Xu, Huifu; Zhang, Dali
作者单位：University of Southampton
摘要：Inspired by a recent work by Alexander et al. (J Bank Finance 30:583-605, 2006) which proposes a smoothing method to deal with nonsmoothness in a conditional value-at-risk problem, we consider a smoothing scheme for a general class of nonsmooth stochastic problems. Assuming that a smoothed problem is solved by a sample average approximation method, we investigate the convergence of stationary points of the smoothed sample average approximation problem as sample size increases and show that w.p...
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作者：Sherali, Hanif D.; Smith, J. Cole
作者单位：Virginia Polytechnic Institute & State University; State University System of Florida; University of Florida
摘要：In this paper, we consider a class of two-stage stochastic risk management problems, which may be stated as follows. A decision-maker determines a set of binary first-stage decisions, after which a random event from a finite set of possible outcomes is realized. Depending on the realization of this outcome, a set of continuous second-stage decisions must then be made that attempt to minimize some risk function. We consider a hierarchy of multiple risk levels along with associated penalties for...
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作者：Lasserre, Jean B.
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We provide a sufficient condition on a class of compact basic semialgebraic sets K subset of R-n for their convex hull co(K) to have a semidefinite representation (SDr). This SDr is explicitly expressed in terms of the polynomials g(j) that define K. Examples are provided. We also provide an approximate SDr; that is, for every fixed epsilon > 0, there is a convex set K-epsilon such that co(K) subset of K-epsilon subset of co(K) + epsilon B (where B is the unit ball of R-n), and K-epsilon has a...
