Second-order sufficient conditions in nonsmooth optimization

Second-order conditions are given which are sufficient to guarantee that a given point be a local solution to certain types of finite-dimensional nonsmooth nonlinear programming problems. Both unconstrained and constrained problems are considered. The conditions of the sufficiency theorems presented here are expressed in terms of the generalized gradients of nonsmooth analysis and (with one exception) certain second-order directional derivatives. These sufficiency theorems are complementary to some necessity theorems, which are proved elsewhere.