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

作者：Li S J^*; Zhu S K; Li X B

来源：Journal of Optimization Theory and Applications, 2012, 155(2): 534-557.

DOI：10.1007/s10957-012-0076-8

• Asymptotic second-order contingent cone
• Second-order derivative
• Semidifferentiable
• Set-valued optimization
• Optimality conditions

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.

• 出版日期2012-11
• 单位重庆大学