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作者：Tseng, Paul; Yun, Sangwoon
作者单位：University of Washington; University of Washington Seattle
摘要：We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained optimization and smooth optimization with l(1)-regularization. We propose a (block) coordinate gradient descent method for solving this class of nonsmooth separable problems. We establish global convergence and, under a local Lipschitzian error bound assumption, linear convergence for this method. The local Lipschitzian error bound holds u...
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作者：Goudou, X.; Munier, J.
作者单位：Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the gradient system x(t) + del Phi(x(t)) = 0 and the so-called heavy ball with friction dynamical system x(t) + lambda x(t) + del Phi(x(t)) = 0, as well as an implicit discrete (proximal) version of it, and study the asymptotic behavior of their solutions in the case of a smooth and quasiconvex objective function Phi. Minimization properties of trajectories are obtained under various additional assumptions. We finally show a minimizing property of the heavy ball method which is no...
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作者：Nguyen, T. T. V.; Strodiot, J. J.; Nguyen, V. H.
作者单位：University of Namur; Vietnam National University Ho Chi Minh City (VNUHCM) System
摘要：We present a bundle method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. First, we consider a general algorithm that we prove to be convergent. Then we explain how to make this algorithm implementable. The strategy is to approximate the nonsmooth convex functions by piecewise linear convex functions in such a way that the subproblems are easy to solve and the convergence is preserved. In particular, we introduce a stopping criterion which is satisf...
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作者：Sorin, Sylvain
作者单位：heSam Universite; Conservatoire National Arts & Metiers (CNAM); Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：The exponential weight algorithm has been introduced in the framework of discrete time on-line problems. Given an observed process {X-m}(m)=1,2,... the input at stage m + 1 is an exponential function of the sum S-m = Sigma(m)(l=1) X-l. We define the analog algorithm for a continuous time process X-t and prove similar properties in terms of external or internal consistency. We then deduce results for discrete time from their counterpart in continuous time. Finally we compare this approach to an...
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作者：van Ngai, Huynh; Thera, Michel
作者单位：Universite de Limoges; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, using the Frechet subdifferential, we derive several sufficient conditions ensuring an error bound for inequality systems in Asplund spaces. As an application we obtain in the context of Banach spaces a global error bound for quadratic nonconvex inequalities and we derive necessary optimality conditions for optimization problems.
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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：Yin, G.; Ion, C.; Krishnamurthy, V.
作者单位：Wayne State University; University of British Columbia
摘要：Stochastic optimization/approximation algorithms are widely used to recursively estimate the optimum of a suitable function or its root under noisy observations when this optimum or root is a constant or evolves randomly according to slowly time-varying continuous sample paths. In comparison, this paper analyzes the asymptotic properties of stochastic optimization/approximation algorithms for recursively estimating the optimum or root when it evolves rapidly with nonsmooth (jump-changing) samp...
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作者：Lasserre, Jean B.
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：Given a compact basic semi-algebraic set K subset of R-n, a rational fraction f : R-n -> R, and a sequence of scalars y = (y(alpha)), we investigate when y(alpha) = integral K x(alpha) f d mu holds for all alpha is an element of N-n, i.e., when y is the moment sequence of some measure f d mu, supported on K. This yields a set of (convex) linear matrix inequalities(LMI). We also use semidefinite programming to develop a converging approximation scheme to evaluate the integral integral f d mu wh...
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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.
