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Applied Mathematics and Optimization

, Volume 5, Issue 1, pp 49–62 | Cite as

Regularity and stability for the mathematical programming problem in Banach spaces

  • J. Zowe
  • S. Kurcyusz
Article

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.

Keywords

Banach Space System Theory Mathematical Method Lagrange Multiplier Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • J. Zowe
    • 1
    • 2
  • S. Kurcyusz
    • 1
    • 2
  1. 1.Institut f. Angew. Mathematik u. StatistikUniversität WürzburgAm HublandWest Germany
  2. 2.Institute of Automatic ControlTechnical University of WarsawWarsawPoland

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