In this paper, new directional regularity conditions are introduced for a general inclusion system involving locally Lipschitz multifunctions. Some sufficient conditions for directional regularities are derived in Hilbert spaces. Second-order necessary conditions for an optimization problem involving locally Lipschitz multifunctions are presented in terms of directional regularity conditions and second-order directional derivatives. An application of the second-order conditions to a mathematical programming problem is presented and some numerical examples are given to illustrate the results.
- Directional regularity
- Second-order directional derivatives
- Second-order necessary conditions
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics