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.
Pini, R., Bianchi, M., Konnov, I. (2017). Barrier methods for equilibrium problems. PURE AND APPLIED FUNCTIONAL ANALYSIS, 2(1), 1-10.
Barrier methods for equilibrium problems
Pini, R;
2017
Abstract
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.
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