Abstract:

In this paper, by using scalarization techniques and a minimax strategy, error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established, where the solutions for vector problems may be general sets under natural assumptions, but are not limited to singletons. The other essentially equivalent approach via a separation principle is analyzed. Special cases to the classical vector equilibrium problem and vector variational inequality are also discussed.

Key words: Generalized mixed vector equilibrium problem ·, Error bounds ·, Gap functions ·, Minimax theorem ·, Scalarization