We consider several versions of the barrier method for a general equilibrium problem with nonlinear constraints in a reflexive Banach space setting. We suggest weak coercivity conditions instead of (generalized) monotonicity, including one containing a perturbed barrier function, in order to entail solutions for the equilibrium problem. We obtain convergence properties of the method under mild assumptions.
|Number of pages||10|
|Journal||PURE AND APPLIED FUNCTIONAL ANALYSIS|
|Publication status||Published - 2017|
- Equilibrium problems
- barrier method
- non-monotone bifunctions
- regularization method