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Generalized equations and their solutions, part II: Applications to nonlinear programming

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Optimality and Stability in Mathematical Programming

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 19))

Abstract

We prove that if the second-order sufficient condition and constraint regularity hold at a local minimizer of a nonlinear programming problem, then for sufficiently smooth perturbations of the constraints and objective function the set of local stationary points is nonempty and continuous; further, if certain polyhedrality assumptions hold (as is usually the case in applications), then the local minimizers, the stationary points and the multipliers all obey a type of Lipschitz condition.

Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation under Grant No. MCS-7901066. Parts of the research for this paper were carried out at the Département de Mathématiques de la Décision, Université Paris-IX Dauphine, with financial support from the Centre National de la Recherche Scientifique, and at the Departamento de Matemáticas y Ciencias de la Computación, Universidad Simón Bolívar, Caracas, Venezuela, with support from the United Nations Educational, Scientific and Cultural Organization under Proyecto UNESCO VEN-77-002. The author greatly appreciates the hospitality and support extended by the institutions cited.

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Authors and Affiliations

  1. University of Wisconsin, 53706, Madison, WI, USA

    Stephen M. Robinson

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  1. Stephen M. Robinson
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Monique Guignard

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© 1982 The Mathematical Programming Society, Inc.

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Robinson, S.M. (1982). Generalized equations and their solutions, part II: Applications to nonlinear programming. In: Guignard, M. (eds) Optimality and Stability in Mathematical Programming. Mathematical Programming Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120989

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  • DOI: https://doi.org/10.1007/BFb0120989

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00849-8

  • Online ISBN: 978-3-642-00850-4

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