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作者：Drummond, L. M. Grana; Maculan, N.; Svaiter, B. F.
作者单位：Universidade Federal do Rio de Janeiro; Universidade Federal do Rio de Janeiro
摘要：We present a geometrical interpretation of the weighting method for constrained (finite dimensional) vector optimization. This approach is based on rigid movements which separate the image set from the negative of the ordering cone. We study conditions on the existence of such translations in terms of the boundedness of the scalar problems produced by the weighting method. Finally, using recession cones, we obtain the main result of our work: a sufficient condition under which weighting vector...
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作者：Todd, M. J.
作者单位：Cornell University
摘要：We observe a curious property of dual versus primal-dual path-following interior-point methods when applied to unbounded linear or conic programming problems in dual form. While primal-dual methods can be viewed as implicitly following a central path to detect primal infeasibility and dual unboundedness, dual methods can sometimes implicitly move away from the analytic center of the set of infeasibility/unboundedness detectors.
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作者：Conn, A. R.; Scheinberg, K.; Vicente, Luis N.
作者单位：Universidade de Coimbra; International Business Machines (IBM); IBM USA
摘要：We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods. These bounds involve a constant that reflects the quality of the interpolation set. The main task of such a derivative free algor...
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作者：Eckstein, Jonathan; Svaiter, B. F.
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：A splitting method for two monotone operators A and B is an algorithm that attempts to converge to a zero of the sum A + B by solving a sequence of subproblems, each of which involves only the operator A, or only the operator B. Prior algorithms of this type can all in essence be categorized into three main classes, the Douglas/Peaceman-Rachford class, the forward-backward class, and the little-used double-backward class. Through a certain extended solution set in a product space, we construct...
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作者：Anstreicher, Kurt M.; Iusem, Alfredo
作者单位：University of Iowa
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作者：Baillon, J. -B.; Cominetti, R.
作者单位：Universidad de Chile; heSam Universite; Universite Pantheon-Sorbonne
摘要：We analyze an equilibrium model for traffic networks based on stochastic dynamic programming. In this model passengers move towards their destinations by a sequential process of arc selection based on a discrete choice model at every intermediate node in their trip. Route selection is the outcome of this sequential process while network flows correspond to the invariant measures of the underlying Markov chains. The approach may handle different discrete choice models at every node, including t...
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作者：Ye, Yinyu
作者单位：Stanford University
摘要：We present polynomial-time interior-point algorithms for solving the Fisher and Arrow - Debreu competitive market equilibrium problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of O(n(4) log(1/epsilon)) for computing an epsilon-equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solution is O(n(4)L) which is in line with the best complexity bound for linear programmi...
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作者：Burachik, Regina S.; Drummond, L. M. Grana; Scheimberg, Susana
作者单位：Universidade Federal do Rio de Janeiro; University of South Australia; Universidade Federal do Rio de Janeiro
摘要：We analyze the logarithmic barrier method for nonsmooth convex optimization in the setting of point-to-set theory. This general framework allows us to both extend and include classical results. We also propose an application for finding efficient points of nonsmooth constrained convex vector-valued problems.
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作者：Scolnik, H. D.; Echebest, N.; Guardarucci, M. T.; Vacchino, M. C.
作者单位：University of Buenos Aires; National University of La Plata
摘要：The authors introduced in previously published papers acceleration schemes for Projected Aggregation Methods (PAM), aiming at solving consistent linear systems of equalities and inequalities. They have used the basic idea of forcing each iterate to belong to the aggregate hyperplane generated in the previous iteration. That scheme has been applied to a variety of projection algorithms for solving systems of linear equalities or inequalities, proving that the acceleration technique can be succe...
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作者：Iusem, Alfredo; Seeger, Alberto
作者单位：Avignon Universite
摘要：Let Xi(H) denote the set of all nonzero closed convex cones in a finite dimensional Hilbert space H. Consider this set equipped with the bounded Pompeiu-Hausdorff metric delta. The collection of all pointed cones forms an open set in the metric space (Xi(H),delta). One possible way of measuring the degree of pointedness of a cone K is by evaluating the distance from K to the set of all nonpointed cones. The number rho(K) obtained in this way is called the radius of pointedness of the cone K. T...
