References of "Mordukhovich, B. S"
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See detailEnhanced metric regularity and Lipschitzian properties of variational systems
Aragón Artacho, Francisco Javier UL; Mordukhovich, B. S.

in Journal of Global Optimization (2011), 50(1), 145-167

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 ... [more ▼]

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 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 (Aragón Artacho and Mordukhovich in Nonlinear Anal 72:1149–1170, 2010) establishing qualitative and quantitative relationships between conventional metric regularity/subregularity 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 op.cit. to partial metric regularity and to the new hemiregularity property. On the other hand, we establish enhanced relationships between certain strong counterparts of metric regularity/hemiregularity and single-valued Lipschitzian localizations. The results obtained are new in both finite-dimensional and infinite-dimensional settings. [less ▲]

Detailed reference viewed: 59 (9 UL)
Full Text
Peer Reviewed
See detailMetric regularity and Lipschitzian stability of parametric variational systems
Aragón Artacho, Francisco Javier UL; Mordukhovich, B. S.

in Nonlinear Analysis: Theory, Methods & Applications (2010), 72(3-4), 1149-1170

The paper concerns the study of variational systems described by parameterized generalized equations/variational conditions important for many aspects of nonlinear analysis, optimization, and their ... [more ▼]

The paper concerns the study of variational systems described by parameterized generalized equations/variational conditions important for many aspects of nonlinear analysis, optimization, and their applications. Focusing on the fundamental properties of metric regularity and Lipschitzian stability, we establish various qualitative and quantitative relationships between these properties for multivalued parts/fields of parametric generalized equations and the corresponding solution maps for them in the framework of arbitrary Banach spaces of decision and parameter variables. [less ▲]

Detailed reference viewed: 67 (5 UL)