Abstract
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.
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