Convex Difference Criteria for the Quantitative Stability of Parametric Quasidifferentiable Systems

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• 作者：A. Uderzo
• 关键词：parametric generalized system ; solution map ; quasidifferential calculus ; convex difference ; Hoffman error bound ; Lipschitz ; like behavior
• 刊名：Set-Valued Analysis
• 出版年：2007
• 出版时间：March, 2007
• 年：2007
• 卷：15
• 期：1
• 页码：81-104
• 全文大小：568 KB

文摘

In this paper solvability and Lipschitzian stability properties for a special class of nonsmooth parametric generalized systems defined in Banach are studied via a variational analysis approach. Verifiable sufficient conditions for such properties to hold under scalar quasidifferentiability assumptions are formulated by combining *-difference and Demyanov difference of convex compact subsets of the dual space with classic quasidifferential calculus constructions. Applications to the formulation of sufficient conditions for metric regularity/open covering of nonsmooth maps, along with their employment in deriving optimality conditions for quasidifferentiable extremum problems, as well as an application to the study of semicontinuity of the optimal value function in parametric optimization are discussed.