Weak sharpness for set-valued variational inequalities and applications to finite termination of iterative algorithms

作者：Xiong, J.; Li, J.^*

来源：Optimization, 2016, 65(8): 1585-1597.

DOI：10.1080/02331934.2016.1160398

• Set-valued variational inequality
• weak sharpness
• finite termination
• maximal monotonicity
• hybrid projection-proximal point algorithm

In this paper, we introduce the notion of weak sharpness for set-valued variational inequalities in the n-dimensional Euclidean space and then present some characterizations of weak sharpness. We also give some examples to illustrate this notion. Under the assumption of weak sharpness, by using the inner limit of a set sequence we establish a sufficient and necessary condition to guarantee the finite termination of an arbitrary algorithm for solving a set-valued variational inequality involving maximal monotone mappings. As an application, we show that the sequence generated by the hybrid projection-proximal point algorithm proposed by Solodov and Svaiter terminates at solutions in a finite number of iterations. These obtained results extend some known results of classical variational inequalities.

• 出版日期2016
• 单位西华师范大学