Necessary and Sufficient Optimality Conditions for Non-regular Problems

We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.