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作者：Brinkhuis, Jan; Zhang, Shuzhong
作者单位：Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Chinese University of Hong Kong
摘要：This paper attempts to extend the notion of duality for convex cones, by basing it on a prescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified conic ordering, defined by a convex cone D, and the inner-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality in the paper...
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作者：Acary, Vincent; Brogliato, Bernard; Goeleven, Daniel
摘要：In this paper we present an extension of Moreau's sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a time-stepping algorithm is also presented. This differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degre...
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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：Jansen, Klaus; Zhang, Hu
作者单位：McMaster University; University of Kiel
摘要：In this paper we present approximation algorithms based on a Lagrangian decomposition via a logarithmic potential reduction to solve a general packing or min-max resource sharing problem with M non-negative convex constraints on a convex set B. We generalize a method by Grigoriadis et al. to the case with weak approximate block solvers ( i.e., with only constant, logarithmic or even worse approximation ratios). Given an accuracy e. ( 0, 1), we show that our algorithm needs O( M( ln M + epsilon...
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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...
