Primal and dual optimality criteria in convex programming

A B S T RAe T This paper considers the problem of minimizing a convex-differentiable function subject to convex differentiable constraints. Necessary and sufficient conditions (not requiring any constraints qualification) for a point to be an optimal solution are given in terms of a parametric I inear program. Dual characterization theorems are then derived, which generalizes the classical results of Kuhn-Tucker and Fritz John.