一类锥约束变分不等式问题的最优性条件

Optimality Conditions for a Class of Variational Inequalities with Cone Constraints

利用像空间分析法,本文研究了带锥约束的变分不等式的最优性条件.利用Gerstewitz非线性标量化函数,给出了三个非线性弱分离函数、两个非线性正则弱分离函数和一个非线性强分离函数.然后,利用此分离函数,得到了带锥约束的变分不等式的弱或强的最优性条件.

In this article, by using the image space analysis, optimality conditions for a class of variational inequalities with cone constraints are proposed. By virtue of the nonlinear scalarization function commonly known as the Gerstewitz function, three nonlinear weak separation functions, two nonlinear regular weak separation functions and a nonlinear strong separation function are introduced. Then, by these nonlinear separation functions, some optimality conditions of the weak and strong alternative for variational inequalities with cone constraints are derived.