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.

Uderzo, A. (2007). Convex difference criteria for the quantitative stability of parametric quasidifferentiable systems. SET-VALUED ANALYSIS, 15(1), 81-104 [10.1007/s11228-006-0035-3].

Convex difference criteria for the quantitative stability of parametric quasidifferentiable systems

UDERZO, AMOS
2007

Abstract

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.
Articolo in rivista - Articolo scientifico
parametric generalized system; solution map; quasidifferential calculus; convex difference; Hoffman error bound; Lipschitz-like behavior
English
mar-2007
15
1
81
104
none
Uderzo, A. (2007). Convex difference criteria for the quantitative stability of parametric quasidifferentiable systems. SET-VALUED ANALYSIS, 15(1), 81-104 [10.1007/s11228-006-0035-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1268
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