Contribution to Dubovitskiy and Milyutin's optimization formalism
This paper is a contribution to the unified approach of Halkin, Neustadt, Gamkrelidze and others to the theory of necessary conditions for general optimization problems.
The basic problem is formulated in terms of real linear topological spaces, mappings between them and a partial ordering determined by a proper convex cone. It includes, therefore, problems with both scalar- and vector-valued optimality criteria.
Optimality conditions are developed in terms of Gâteaux and Fréchet differentials of given mappings and linear continuous functionals on the spaces concerned, making use of the Dubovitskiy and Milyutin's formalism.
KeywordsBanach Space Convex Cone SIAM Journal Separation Theorem Polar Cone
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