Second-Order Necessary Conditions in Constrained Semismooth Optimization
Robin W. Chaney · SIAM Journal on Control and Optimization · 1987
First- and second-order conditions are given which must necessarily be satisfied by local minimizers for certain finite-dimensional nonsmooth nonlinear programming problems. The problems considered are of standard form, having a finite number of equality and inequality constraints. The principal result does not require a constraint qualification, but does require that the functions be semismooth at the minimizer. The necessary conditions are stated in terms of the generalized gradients of nonsmooth analysis and certain second-order directional derivatives.