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Regularity and stability for the mathematical programming problem in Banach spaces

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Abstract

This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on the active part only of the constraint, and that it is preserved under small perturbations. Moreover, we show that our condition is “almost” equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers. The main step in the proof of our results is a generalization of the open mapping theorem.

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Authors and Affiliations

  1. Institut f. Angew. Mathematik u. Statistik, Universität Würzburg, 8700 Würzburg, Am Hubland, West Germany

    J. Zowe & S. Kurcyusz

  2. Institute of Automatic Control, Technical University of Warsaw, Warsaw, Poland

    J. Zowe & S. Kurcyusz

Authors
  1. J. Zowe
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  2. S. Kurcyusz
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Additional information

Communicated by J. Stoer

The early parts of this article result from fruitful correspondence with S. Kurcyusz, who died tragically in 1978. This paper is dedicated to his memory.

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Zowe, J., Kurcyusz, S. Regularity and stability for the mathematical programming problem in Banach spaces. Appl Math Optim 5, 49–62 (1979). https://doi.org/10.1007/BF01442543

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  • DOI: https://doi.org/10.1007/BF01442543

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