Second-order necessary conditions for inequality and equality constrained C1, 1 optimization problems are derived. A constraint qualification condition which uses the recent generalized second-order directional derivative is employed to obtain these conditions. Various second-order sufficient conditions are given under appropriate conditions on the generalized second-order directional derivative in a neighborhood of a given point. An application of the second order conditions to a new class of nonsmooth C1, 1 optimization problems with infinitely many constraints is presented.
ASJC Scopus subject areas
- Signal Processing
- Computer Science Applications
- Control and Optimization