Second-order necessary conditions in locally Lipschitz optimization with inequality constraints
The author studies a nonsmooth scalar optimization problem involving finitely many inequality constraints. Primal necessary optimality conditions in terms of second-order directional derivatives are derived in the case that the objective function and active constraints are locally Lipschitz at the extremum point. Dual necessary optimality conditions via second-order directional derivatives are established in the case that the objective function and active constraints are locally Lipschitz, regular in the sense of Clarke and Gâteaux differentiable at the extremum point. The results obtained here are generalizations of some recent results by I. Ginchev and V. I. Ivanov.
scientific article; zbMATH DE number 6418510
scientific article