Constructive Generalization of Classical Sufficient Second-Order Optimality Conditions

Abstract

New sufficient second-order optimality conditions for equality constrained optimization problems are proposed, which significantly strengthen and complement classical ones and are constructive. For example, they establish the equivalence between sufficient conditions for inequality constrained optimization problems and sufficient conditions for optimality in equality constrained problems by reducing the former to equalities via introducing slack variables. Previously, in the case of classical sufficient optimality conditions, this fact was not considered to be true, that is, the existing classical sufficient conditions were not complete. Accordingly, the proposed optimality conditions complement the classical ones and solve the issue of equivalence between inequality and equality constrained problems when the former is reduced to the latter by introducing slack variables.