An interior proximal cutting hyperplane method for equilibrium problems
Department of Mathematics Education, Kyungnam University, Masan, Kyungnam, 631-701, Korea
Journal of Inequalities and Applications 2012, 2012:99 doi:10.1186/1029-242X-2012-99Published: 23 April 2012
We propose a new method for solving equilibrium problems on polyhedra, where the underlying function is continuous and satisfies a pseudomonone assumption which is called an interior proximal cutting hyperplane method. The method is based on the special interior proximal function which replaces the usual quadratic function. This leads to an interior proximal algorithm. The algorithm can be viewed as combining the cutting hyperplane method and the special interior proximal function. Finally some preliminary computational results are given.
AMS Mathematics Subject Classification 2000: 65K10; 90 C25.