Criticality of Lagrange Multipliers in Variational Systems
Boris S. Mordukhovich, Ebrahim Sarabi · SIAM Journal on Optimization · 2019
The paper concerns the study of criticality of Lagrange multipliers in variational systems, which has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and the like, we focus on general nonpolyhedral systems that are associated, in particular, with problems of conic programming. Developing a novel approach that is mainly based on advanced techniques and tools of second-order variational analysis and generalized differentiation allows us to overcome the principal challenges of nonpolyhedrality and to establish complete characterizations on noncritical multipliers in such settings. The results are illustrated by examples from semidefinite programming.