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.
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References
Kurcyusz, S.,On the Existence and Nonexistence of Lagrange Multipliers in Banach Spaces, Journal of Optimization Theory and Applications, Vol. 20, No. 1, 1976.
Schaefer, H. H.,Topological Vector Spaces, The Macmillan Company, New York, New York, 1966.
Robinson, S. M.,Regularity and Stability for Convex Multivalued Functions, Mathematics of Operations Research, Vol. 1, No. 2, 1976.
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Communicated by O. L. Mangasarian
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Zowe, J. A remark on a regularity assumption for the mathematical programming problem in Banach spaces. J Optim Theory Appl 25, 375–381 (1978). https://doi.org/10.1007/BF00932900
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DOI: https://doi.org/10.1007/BF00932900