Some Sufficient Optimality Conditions in Nonsmooth Analysis
Andrew C. Eberhard, Robert Wenczel · SIAM Journal on Optimization · 2009
In this paper we study some second order conditions that may be added to the first order nessessary optimality condition $0\in\partial_{p}f(\bar{x})$ (with $\partial_{p}f$ denoting the proximal subdifferential) in order to obtain a sufficient condition for a strict local minimum for extended–real-valued, nonsmooth functions. Three different types of second order conditions are investigated, all based on a different second order subdifferential. Namely, the subhessian, the graphical derivative, and the (contingent) coderivative to the proximal subdifferential.