Levitin–Polyak Well-Posedness of Vector Variational Inequality Problems with Functional Constraints

Abstract

The Levitin–Polyak well-posedness for a constrained problem guarantees that, for an approximating solution sequence, there is a subsequence which converges to a solution of the problem. In this article, we introduce several types of (generalized) Levitin–Polyak well-posednesses for a vector variational inequality problem with both abstract and functional constraints. Various criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posednesses are presented.

Keywords:

• Approximating solution sequence
• Cone-monotonicity
• Cone-coercivity
• Generalized Levitin–Polyak well-posedness
• Vector variational inequality with functional constraints

AMS Subject Classification:

• 49K40
• 90C30
• 90C31

ACKNOWLEDGMENTS

This work is supported by the Research Grants Council of Hong Kong (PolyU 5317/07E) and the National Science Foundation of China.