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Summary: Journal of Global Optimization 24: 285309, 2002.
c 2002 Kluwer Academic Publishers. Printed in the Netherlands.
Gradient Approach of Computing Fixed Points of
Equilibrium Problems
ANATOLY ANTIPIN
Computing Center of Russian Academy of Sciences, Vavilov str. 40, 117967 Moscow,
Russia
(e-mail: antipin@ccas.ru)
Revised 28 November 2003
Abstract. Potential equilibrium problems are considered. The notions of bilinear dierential
and bi-convexity are introduced. The concept of generalized potentiality is oered. The con-
vergence of gradient prediction-type methods for solving of generalized potential equilibrium
problems is justied. Estimates of convergence rate are derived.
Key words: Equilibrium programming problem, xed point, gradient approach, symmetry,
skew-symmetry
1. Statement of problem
Let us consider the problem of computing a xed point v
0 of extreme mapping [7],[8]
v
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