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Full-Text Articles in Mathematics
Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina
Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina
Mathematics Research Reports
Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.
Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich
Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich
Mathematics Research Reports
This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …
Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang
Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang
Mathematics Research Reports
The primary goal of this paper is to study some notions of normals to nonconvex sets in finite-dimensional and infinite-dimensional spaces and their images under single-valued and set-valued mappings. The main motivation for our study comes from variational analysis and optimization, where the problems under consideration play a crucial role in many important aspects of generalized differential calculus and applications. Our major results provide precise equality formulas (sometimes just efficient upper estimates) allowing us to compute generalized normals in various senses to direct and inverse images of nonconvex sets under single-valued and set-valued mappings between Banach spaces. The main tools …
Failure Of Metric Regularity For Major Classes Of Variational Systems, Boris S. Mordukhovich
Failure Of Metric Regularity For Major Classes Of Variational Systems, Boris S. Mordukhovich
Mathematics Research Reports
The paper is devoted to the study of metric regularity, which is a remarkable property of set-valued mappings playing an important role in many aspects of nonlinear analysis and its applications. We pay the main attention to metric regularity of the so- called parametric variational systems that contain, in particular, various classes of parameterized/perturbed variational and hemivariational inequalities, complementarity systems, sets of optimal solutions and corresponding Lagrange multipliers in problems of parametric optimization and equilibria, etc. Based on the advanced machinery of generalized differentiation1 we surprisingly reveal that metric regularity fails for certain major classes of parametric variational systems, which …