Optimality conditions for piecewiseC 2 nonlinear programming

Several types of finite-dimensional nonlinear programming models are considered in this article. Second-order optimality conditions are derived for these models, under the assumption that the functions involved are piecewiseC². In rough terms, a real-valued function defined on an open subsetW orRⁿ is said to be piecewiseC^k onW if it is continuous onW and if it can be constructed by piecing together onW a finite number of functions of classC^k.