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Local monotonicity and full stability for parametric variational systems

Boris Mordukhovich (boris***at***math.wayne.edu)
Tran Nghia (nttran***at***oakland.edu)

Abstract: The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, postulated certain quantitative properties of single-valued localizations of solution maps, are closely related to local strong maximal monotonicity of associated set-valued mappings. Based on advanced tools of variational analysis and generalized differentiation, we derive verifiable characterizations of the local strong maximal monotonicity and full stability notions under consideration via some positive-definiteness conditions involving second-order constructions of variational analysis.

Keywords: Full stability, Parametric variational systems, local maximal monotonicity

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 09/06/2015
Entry Accepted: 09/06/2015
Entry Last Modified: 09/06/2015

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