SOLVABILITY OF A PERTURBED VARIATIONAL INEQUALITY

作者：Li Fenglian; He Yiran^*

来源：Pacific Journal of Optimization, 2014, 10(1): 105-111.

• variational inequality
• set-valued mapping
• upper semicontinuous mapping
• variational inequality property
• perturbation

This paper aims to establish solvability of a perturbed variational inequality defined by a set-valued mapping without assuming any kind of monotonicity. It is shown that if a coercivity condition holds, then the perturbed variational inequality has a solution. Two main results are obtained. The coercivity condition assumed in the first result implies the solution set of the variational inequality is nonempty and bounded, and that in the second one implies only the existence-of solution. The first result extends some known results, while the second result is new even if the mapping is single-valued.

• 出版日期2014-1
• 单位四川师范大学