Quantitative analysis of a subgradient-type method for equilibrium problems

Abstract

We use techniques originating from the subdiscipline of mathematical logic called 'proof mining' to provide rates of metastability and -under a metric regularity assumption -rates of convergence for a subgradienttype algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence.