On gap functions for equilibrium problems via Fenchel duality. (English) Zbl 1103.49016

Summary: We deal with the construction of gap functions for equilibrium problems by using the Fenchel duality theory for convex optimization problems. For proving the properties which characterize a gap function weak and strong duality are used. Moreover, the proposed approach is applied to variational inequalities in a real Banach space.


49N15 Duality theory (optimization)
58E35 Variational inequalities (global problems) in infinite-dimensional spaces
90C25 Convex programming