The authors consider the following nonlinear programming problem:
where q(x), X is an open subset of and , are differentiable functions. The aim of the paper is to give a set of conditions which are both necessary and sufficient for optimality in problem (1). It is shown (under some additional assumptions) that is optimal for (1) if and only if the Kuhn-Tucker conditions hold at and there exists a function : , , such that and for all . Necessary and sufficient conditions are also given for optimality of the problem dual to (1).