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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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