Second‐Order Optimality Conditions for Strict Efficiency of Constrained Set‐Valued Optimization

In this paper, we propose several second‐order derivatives for set‐valued maps and discuss their properties. By using these derivatives, we obtain second‐order necessary optimality conditions for strict efficiency of a set‐valued optimization problem with inclusion constraints in real normed spaces. We also establish second‐order sufficient optimality conditions for strict efficiency of the set‐valued optimization problem in finite‐dimensional normed spaces. As applications, we investigate second‐order sufficient and necessary optimality conditions for a strict local efficient solution of order two of a nonsmooth vector optimization problem with an abstract set and a functional constraint.