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作者：Gowda, M. Seetharama; Tao, Jiyuan
作者单位：University System of Maryland; University of Maryland Baltimore
摘要：Motivated by the similarities between the properties of Z-matrices on R-+(n) and Lyapunov and Stein transformations on the semidefinite cone S-+(n), we introduce and study Z-transformations on proper cones. We show that many properties of Z-matrices extend to Z-transformations. We describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations. Finally, we study the equivalence of Q and P properties of Z-transformations on symmetric cones. In ...
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作者：Iusem, Alfredo N.; Kassay, Gabor; Sosa, Wilfredo
作者单位：Babes Bolyai University from Cluj; University Nacional de Ingenieria Lima
摘要：The main purpose of this paper is the study of sufficient and/or necessary conditions for existence of solutions of equilibrium problems. We discuss some of the assumptions of the problem, under which the introduced conditions are sufficient and/or necessary, and also analyze the effect of these assumptions on the connection between the solution sets of the equilibrium problem and of a related convex feasibility problem.
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作者：Dontchev, A. L.; Rockafellar, R. T.
作者单位：University of Washington; University of Washington Seattle
摘要：S. M. Robinson published in 1980 a powerful theorem about solutions to certain generalized equations corresponding to parameterized variational inequalities which could represent the first-order optimality conditions in nonlinear programming, in particular. In fact, his result covered much of the classical implicit function theorem, if not quite all, but went far beyond that in ideas and format. Here, Robinson's theorem is viewed from the perspective of more recent developments in variational ...
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作者：Grodzevich, Oleg; Wolkowicz, Henry
作者单位：University of Waterloo; University of Waterloo
摘要：We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional trust-region subproblem, TRS, approach that makes use of the L-curve maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We apply a parameterized trust region approach to estimate the region of maximum curvature of the L-curve and find the regularized so...
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作者：Chen, Xiaojun; Zhang, Chao; Fukushima, Masao
作者单位：Kyoto University; Hirosaki University
摘要：We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty and bounded solution set. We give a new error bound for the monotone LCP and use it to show that solu...
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作者：Burke, James V.; Deng, Sien
作者单位：University of Washington; University of Washington Seattle; Northern Illinois University
摘要：The notion of weak sharp minima unifies a number of important ideas in optimization. Part I of this work provides the foundation for the theory of weak sharp minima in the infinite-dimensional setting. Part II discusses applications of these results to linear regularity and error bounds for nondifferentiable convex inequalities. This work applies the results of Part I to error bounds for differentiable convex inclusions. A number of standard constraint qualifications for such inclusions are al...
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作者：Attouch, Hedy; Cominetti, Roberto; Teboulle, Marc
作者单位：Universidad de Chile; Universite de Montpellier; Tel Aviv University
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作者：Guerkan, Guel; Pang, Jong-Shi
作者单位：Tilburg University; Rensselaer Polytechnic Institute
摘要：Inspired by previous works on approximations of optimization problems and recent papers on the approximation of Walrasian and Nash equilibria and on stochastic variational inequalities, the present paper investigates the approximation of Nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach, a variational approach, and an optimization approach. Besides directly addressing the issue of convergence of Nash equilibria via app...
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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...
