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Generalized Kuhn–Tucker conditions stated in this paper correspond to the optimality conditions for mathematical programming problems in a Banach space. Constraint qualifications given before can be regarded as special cases of the present constraint qualification introduced to prove the necessity. Pseudoconvexity of the constraint set rather than convexity is required for sufficiency. In case this hypothesis fails to be satisfied, second order optimality conditions are sufficient for an isolated local optimum.
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Monique Guignard (1969) studied this question.
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