Boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems with an application.

Zhong, Ren-You; Huang, Nan-Jing; Cho, Yeol Je

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Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ...