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First-order optimality conditions in generalized semi-infinite programming. (English) Zbl 0956.90055
Summary: The authors consider a generalized semi-infinite optimization problem where the index set of corresponding inequality constraints depends on the decision variables and the involved functions are assumed to be continuously differentiable. We derive first-order necessary optimality conditions for such problems by using bounds for the upper and lower directional derivatives of the corresponding optimal value function. In the case where the optimal value function is directly differentiable, we present first-order conditions based on the linearization of the given problem. Finally, we investigate necessary and sufficient first-order conditions by using the calculus of quasidifferentiable functions.

MSC:
90C34Semi-infinite programming
90C46Optimality conditions, duality