Exceptional family of elements for generalized variational inequalities

作者：Liu Zhi; He Yiran^*

来源：Journal of Global Optimization, 2010, 48(3): 465-471.

DOI：10.1007/s10898-009-9500-5

• Generalized variational inequality
• Topological degree
• Exceptional family of elements
• Coercivity condition

This paper introduces a new concept of exceptional family of elements for a finite-dimensional generalized variational inequality problem. Based on the topological degree theory of set-valued mappings, an alternative theorem is obtained which says that the generalized variational inequality has either a solution or an exceptional family of elements. As an application, we present a sufficient condition to ensure the existence of a solution to the variational inequality. The set-valued mapping is assumed to be upper semicontinuous with nonempty compact convex values.

• 出版日期2010-11
• 单位四川师范大学