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Exact penalty functions in nonlinear programming

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Abstract

It is shown that the existence of a strict local minimum satisfying the constraint qualification of [16] or McCormick's [12] second order sufficient optimality condition implies the existence of a class of exact local penalty functions (that is ones with a finite value of the penalty parameter) for a nonlinear programming problem. A lower bound to the penalty parameter is given by a norm of the optimal Lagrange multipliers which is dual to the norm used in the penalty function.

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Authors and Affiliations

  1. University of Illinois, Urbana, Illinois, USA

    S. -P. Han

  2. University of Wisconsin, Madison, Wisconsin, USA

    O. L. Mangasarian

Authors
  1. S. -P. Han
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  2. O. L. Mangasarian
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Additional information

Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation under Grant No. MCS74-20584 A02.

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Han, S.P., Mangasarian, O.L. Exact penalty functions in nonlinear programming. Mathematical Programming 17, 251–269 (1979). https://doi.org/10.1007/BF01588250

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  • DOI: https://doi.org/10.1007/BF01588250

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