Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis

Author:
Boris Mordukhovich

Journal:
Trans. Amer. Math. Soc. **343** (1994), 609-657

MSC:
Primary 49J52; Secondary 49K40, 90C31

DOI:
https://doi.org/10.1090/S0002-9947-1994-1242786-4

MathSciNet review:
1242786

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions. These objects have a wide range of applications in optimization, nonlinear analysis, mathematical economics, etc. Our main concern is Lipschitzian stability of multivalued solution maps depending on parameters. We employ a new approach of nonsmooth analysis based on the generalized differentiation of multivalued and nonsmooth operators. This approach allows us to obtain effective sufficient conditions as well as necessary and sufficient conditions for a natural Lipschitzian behavior of solution maps. In particular, we prove new criteria for the existence of Lipschitzian multivalued and single-valued implicit functions.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1242786-4

Keywords:
Generalized equations,
variational inequalities,
stability and sensitivity,
nonsmooth analysis,
generalized differentiation

Article copyright:
© Copyright 1994
American Mathematical Society