ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints

摘要: In this paper, e-optimality conditions are given for a nonconvex programming problem which has an infinite number of constraints. The objective function and the constraint functions supposed to be locally Lipschitz on Banach space. first part, we introduce concept regular e-solution propose generalization Karush-Kuhn-Tucker conditions. These up e obtained by weakening classical complementarity Furthermore, they satisfied without assuming any qualification. Then, prove that these also sufficient when constraints convex is e-semiconvex. second define quasisaddlepoints associated with e-Lagrangian functional investigate their relationships generalized KKT particular, formulate Wolfe-type dual allows us present e-duality theorems between e-solutions dual. Finally, apply results two important problems: cone-constrained semidefinite problem.