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A remark on a regularity assumption for the mathematical programming problem in Banach spaces

Contributed Papers

Abstract

This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces.

Key Words

Mathematical programming Slater regularity condition Lagrange multipliers functional analysis 

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References

  1. 1.
    Kurcyusz, S.,On the Existence and Nonexistence of Lagrange Multipliers in Banach Spaces, Journal of Optimization Theory and Applications, Vol. 20, No. 1, 1976.Google Scholar
  2. 2.
    Schaefer, H. H.,Topological Vector Spaces, The Macmillan Company, New York, New York, 1966.Google Scholar
  3. 3.
    Robinson, S. M.,Regularity and Stability for Convex Multivalued Functions, Mathematics of Operations Research, Vol. 1, No. 2, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • J. Zowe
    • 1
  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgWest Germany

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