Abstract
The purpose of this paper is to investigate coderivatives of the gap function involving the Minty vector variational inequality. First, we discuss the regular coderivative, the normal coderivative, and the mixed coderivative of a class of set-valued maps. Then, by using the relationships between the coderivatives of a set-valued map and its efficient points set-valued map, we obtain the coderivatives of the gap function for the Minty vector variational inequality.
Highlights
The vector variational inequality and the Minty vector variational inequality have been of great interest in the academic and professional communities ever since the path-breaking paper [ ] in the early s
There are some applications to be found in vector traffic equilibrium problems
It is well known that the concept of gap functions is very important for the study of (VVI) and (MVVI)
Summary
The vector variational inequality (for short, VVI) and the Minty vector variational inequality (for short, MVVI) have been of great interest in the academic and professional communities ever since the path-breaking paper [ ] in the early s. From the vector optimization point of view, Chen et al [ ] defined the gap function for the (VVI) problem as a set-valued map.
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