Necessary Conditions for Constrained Optimization Problems in Smooth Banach Spaces and Applications
Qiji Jim Zhu · SIAM Journal on Optimization · 2002
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.