Differential properties and optimality conditions for generalized weak vector variational inequalities

作者：Zhu S K^*; Li S J; Teo K L

来源：Positivity, 2013, 17(3): 443-457.

DOI：10.1007/s11117-012-0179-3

• Contingent derivative
• Gap function
• Generalized weak vector variational inequality
• Optimality conditions

In this paper, we study a generalized weak vector variational inequality, which is a generalization of a weak vector variational inequality and a Minty weak vector variational inequality. By virtue of a contingent derivative and a I broken vertical bar-contingent cone, we investigate differential properties of a class of set-valued maps and obtain an explicit expression of its contingent derivative. We also establish some necessary optimality conditions for solutions of the generalized weak vector variational inequality, which generalize the corresponding results in the literature. Furthermore, we establish some unified necessary and sufficient optimality conditions for local optimal solutions of the generalized weak vector variational inequality. Simultaneously, we also show that there is no gap between the necessary and sufficient conditions under an appropriate condition.

• 出版日期2013-9
• 单位重庆大学