Necessary Conditions for Constrained Optimization Problems in Smooth Banach Spaces and Applications

Q. J. Zhu

Abstract: We derive necessary optimality conditions for constrained minimization problems with lower semicontinuous inequality constraints, continuous equality constraints and a set constraint in smooth Banach spaces. Then we apply these necessary optimality conditions to derive
subdifferential characterizations of singular normal vectors to the epigraph and the graph of a function, subdifferential calculus, and necessary optimality conditions for mathematical programs with equilibrium constraints.

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