一类向量变分不等式组解的刻画及弱尖极小

Characterizations and Weak Sharp Minima for a System of Solutions for Vector Variational Inequality

向量变分不等式(VVI)是Giannessi首先在有限维欧几里得空间中引入的。随后,由Chen将其推广到无穷维空间中并进行研究。近年来,(VVI)得到了广泛的研究,其解的性质得到了刻画,其解的弱尖极小已经在强单调条件下得到了证明。该文研究了一类向量变分不等式组,在PPM条件下(F和-F都是伪单调),对其解进行了一些刻画此外,给出了该向量变分不等式组的一个间隙函数,并在强单调条件下,证明了它是弱尖极小的。

Vector variational inequality （VVI）, as an important generalization of the classical variational inequality, was first introduced and studied by Giannessi in the finite dimensional Euclidean spaces. Then, it was studied and generalized in infinite dimensional spaces by Chen. Recently, some characterizations of solutions of VVI and its weak sharp minima under strong monotonicity have been proved. In this paper, some characterizations of solutions for a system of vector variational inequalities are derived under the assumption of PPM （where F and -F are both pseudomonotone）. Moreover, a gap function for this system of vector variational inequalities is suggested and proved to be weak sharp minima under strong monotonieity.