On sufficient conditions for local optimality in semi-infinite programming
Hubertus Th. Jongen, Wolfgang Wetterling, G. Zwier · Optimization · 1987
We state two new second order sufficient conditions for local strict optimality in semi-infinite programming, which do not require a strict complementarity condition for the local reduction of the feasible set. This set will be described (locally) by means of a finite number of local optimal value functions, Due to the lack of strict complementarity, the latter functions are only of differentiability class C 1We show how the unique solution of a parametric nonlinear programming problem with inequalities is glued together from C 1piece of unique solutions of problems with only equally constraints. As a consequence, the local optimal value functions will be piecewise of class C 2, which gives information of second order.