A NECESSARY AND SUFFICIENT CONSTRAINT QUALIFICATION FOR SUFFICIENT OPTIMALITY CONDITIONS IN DIFFERENTIABLE PROGRAMMING

In this paper, we study qualifications imposed on the constraints in order to validate the Karush-Kuhn-Tucker sufficient optimality conditions in differentiable minimization programming. Such qualifications are called constraint qualifications for sufficient optimality conditions in this study. We propose a weak constraint qualification for sufficient optimality conditions, which is necessary and sufficient for the Karush-Kuhn-Tucker sufficient optimality conditions to be valid for any objective function which is pseudoconvex at the minimum point. Also, we consider differentiable multiobjective programming whose objective function is assumed some convexity condition and we show the constraint qualification is also a necessary and sufficient constraint qualification for sufficient conditions of Pareto optimality and weak Pareto optimality.