Abstract
Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions.
Highlights
The concept of the vector variational inequality (VVI, for short) was first introduced by Giannessi in his well-known paper [1]
Continuity results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions
Error bounds for the weak vector variational inequality in terms of two known regularized gap functions are obtained, under strong pseudomonotonicity assumptions
Summary
The concept of the vector variational inequality (VVI, for short) was first introduced by Giannessi in his well-known paper [1]. Our interest in this paper is to further discuss the continuity (both upper and lower semicontinuities) of solution mappings for parametric VVIs and error bounds for weak VVIs in terms of the known regularized gap functions. Wang and Huang [10] have discussed the lower semicontinuity of the weak Pareto/efficient solutions to a parametric vector mixed variational inequality under a kind of strict pseudomonotonicity assumptions. We will further study the continuity (both lower and upper semicontinuities) of the Pareto/efficient solution mapping for a parametric VVI with a polyhedral constraint set discussed in our previous work [12], within the framework of strict pseudomonotonicity assumptions.
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