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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：Mordukhovich, B. S.
作者单位：Wayne State University
摘要：The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mai...
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作者：Hager, William W.; Mair, Bernard A.; Zhang, Hongchao
作者单位：State University System of Florida; University of Florida; University of Minnesota System; University of Minnesota Twin Cities
摘要：We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled cyclic Barzilai-Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order sufficient optimality conditions are satisfied. Numerical experiments show that the convergence speed is insensiti...
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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：Mordukhovich, Boris; Nemirovski, Arkadi; Nesterov, Yurii
作者单位：University System of Georgia; Georgia Institute of Technology; Wayne State University; Universite Catholique Louvain
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作者：Barty, Kengy; Roy, Jean-Sebastien; Strugarek, Cyrille
作者单位：Electricite de France (EDF)
摘要：We focus on the numerical solution of closed-loop stochastic problems, and propose a perturbed gradient algorithm to achieve this goal. The main hurdle in such problems is the fact that the control variables are infinite-dimensional, due to, e.g., the information constraints. Alternatively said, control variables are feedbacks, i.e., functions. Such controls have hence to be represented in a finite way in order to solve the problem numerically. In the same way, the gradient of the criterion is...
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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...
