Second-order optimality conditions for the extremal problem under inclusion constraints

In this paper we establish second-order necessary and sufficient conditions for the problem of minimizing a functionf on the solution set of an inclusion 0∈F(x) wheref and the support function of set-valued mapF areC1,1-functions, i.e., functions whose gradient mapping is locally Lipschitz. Our results generalize those obtained by Hiriart-Urruty and others.