Abstract

Metric subregularity and regularity of multifunctions are fundamental notions in variational analysis and optimization. Using the concept of strong slope, in this paper we first establish a criterion for metric subregularity of multifunctions between metric spaces. Next, we use a combination of abstract coderivatives and contingent derivatives to derive verifiable first order conditions ensuring metric subregularity of multifunctions between Banach spaces. Then using second order approximations of convex multifunctions, we establish a second order condition for metric subregularity of mixed smooth-convex constraint systems, which generalizes a result established recently by Gfrerer [Gfrerer H (2011) First order and second order characterizations of metric subregularity and calmness of constraint set mapping. SIAM J. Optim. 21(4):1439–1474].