Abstract
The formalism of Dubovitskii and Milyutin is very attractive but, up to now, it could not be applied to optimization problems involving equality and operator constraints. In the present paper, the formalism of Dubovitskii and Milyutin is extended to this more general situation. Theorem 2.1, the main result of the paper, is applied to the standard mathematical programming problem in normed linear space and an abstract maximum principle is obtained.
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This research was sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, USAF, under Grant No. AFOSR-68-1529A. The author thanks Dr. K. Makowski for several valuable comments of an earlier draft of the present paper.
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Halkin, H. A satisfactory treatment of equality and operator constraints in the Dubovitskii-Milyutin optimization formalism. J Optim Theory Appl 6, 138–149 (1970). https://doi.org/10.1007/BF00927047
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DOI: https://doi.org/10.1007/BF00927047