This work is part of an ongoing effort comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general NLP with equality and inequality constraints relation equivalent MPCC reformulation. show that kink qualifications constraint linear independence type Mangasarian-Fromovitz are equivalent. Then we consider strong stationarity concepts first second order optimality ...

In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower-semicontinuous function and the precomposition of another convex lower-semicontinuous function which is also K-increasing with a K-convex K-epi-closed function, where K is a non-empty closed convex cone. These statements prove to be...

Mathematical programs with equilibrium (or complementarity) constraints (MPECs for short) form a difficult class of optimization problems. The standard KKT conditions are not always necessary optimality conditions due to the fact that suitable constraint qualifications are often violated. Alternatively, one can therefore use the Fritz John-approach to derive necessary optimality conditions. Whi...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the "badly behaved set" of constraints, i.e. the set of constraints which causes problems in the Kuhn-Tucker theory, is isolated and a computational procedure for checking whether a...