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Full Stability in Finite-Dimensional Optimization

Boris Mordukhovich(boris***at***math.wayne.edu)
Nghia Tran(nghia***at***math.wayne.edu)
Tyrrell Rockafellar(rtr***at***math.washington.edu)

Abstract: The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems including those of conic and specifically semidefinite programming. Developing a new technique of variational analysis and generalized differentiation, we derive second-order characterizations of full stability, in both Lipschitzian and H\"olderian settings, and establish their relationships with the conventional notions of strong regularity and strong stability for a large class of problems of constrained optimization with twice continuously differentiable data.

Keywords: constrained optimization; full stability; variational analysis; generalized differentiation; conic programming; semidefinite programming; strong regularity; strong stability

Category 1: Convex and Nonsmooth Optimization

Citation:

Download: [PDF]

Entry Submitted: 07/14/2013
Entry Accepted: 07/14/2013
Entry Last Modified: 07/14/2013

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