Error bounds for generalized Lagrange multipliers in locally Lipschitz programming

  • M. Pappalardo
Technical Note

Abstract

Recent studies are concerned with two types of questions in nonconvex optimization: (a) conditions for having bounded Lagrange multipliers, Refs. 1–2; (b) a priori bounds for such Lagrange multipliers, Ref. 3. Such topics have been investigated under suitable regularity assumptions. The purpose of this paper is to study the same problems for the generalized Lagrange multipliers of a locally Lipschitz programming.

Key Words

Generalized Lagrange multipliers generalized derivatives Lipschitz programming 

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References

  1. 1.
    Gauvin, J.,A Necessary and Sufficient Regularity Condition to Have Bounded Multipliers in Nonconvex Programming, Mathematical Programming, Vol. 12, pp. 136–138, 1977.Google Scholar
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    Nguyen, V. H., Strodiot, J. J., andMifflin, R.,On Conditions to Have Bounded Multipliers in Locally Lipschitz Programming, Mathematical Programming, Vol. 18, pp. 100–106, 1980.Google Scholar
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    Mangasarian, O. L.,Computable Numerical Bounds for Lagrange Multipliers of Stationary Points of Nonconvex Differentiable Nonlinear Programs, Operations Research Letters, Vol. 4, pp. 47–48, 1985.Google Scholar
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    Clarke, F. H.,Optimization and Nonsmooth Analysis, Wiley, New York, New York, 1983.Google Scholar
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    Hiriart-Urruty, J. B.,Refinements of Necessary Optimality Conditions in Nondifferentiable Programming, I, Applied Mathematics and Optimization, Vol. 5, pp. 63–82, 1979.Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • M. Pappalardo
    • 1
  1. 1.Department of MathematicsUniversity of PisaPisaItaly

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