ABSTRACT
Using results of Avakov about tangent directions to equality constraints given by smooth operators, we formulate a theory of first and second order conditions for optimality in the sense of Dubovitskii-Milyutin which is nontrivial also in the case of equality constraints given by nonregular operators. Second order feasible and tangent directions are defined to construct conical approximations to inequality and equality constraints. In particular, the result generalizes Avakov’s result for the smooth case.
