Abstract
The paper deals with the existence of Lagrange multipliers for a general nonlinear programming problem. Some regularity conditions are formulated which are, in a sense, the weakest to assure the existence of multipliers. A number of related conditions are discussed. The connection between the choice of suitable function spaces and the existence of multipliers is analyzed.
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Communicated by O. L. Mangasarian
This work was partly supported by the National Science Foundation, Grant No. GF-37298, to the Institute of Automatic Control, Technical University of Warsaw, Warsaw, Poland, and the Department of Computer and Control Sciences, University of Minnesota, Minneapolis, Minnesota.
The author wishes to thank Professor A. P. Wierzbicki for many important remarks concerning the subject of this paper.
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Kurcyusz, S. On the existence and nonexistence of Lagrange multipliers in Banach spaces. J Optim Theory Appl 20, 81–110 (1976). https://doi.org/10.1007/BF00933349
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DOI: https://doi.org/10.1007/BF00933349