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On equilibrium problems. (English) Zbl 1064.49009
Summary: Some iterative methods for solving equilibrium problems are suggested and analyzed by using the technique of the auxiliary principle. We have shown that the convergence of the proposed methods either requires only pseudomonotonicity, which is a weaker condition than monotonicity or partially relaxed strongly monotonicity. Our results represent an improvement and refinement of previously known results. Since the equilibrium problems include variational inequalities and complementarity problems as special cases, the results proved in this paper continue to hold for these problems.
MSC:
49J40Variational methods including variational inequalities
47N10Applications of operator theory in optimization, convex analysis, programming, economics
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)