The subgradient extragradient method for pseudomonotone equilibrium problems

ABSTRACT

In this paper, an improvement of the extragradient algorithm is considered for finding a solution of pseudo-monotone equilibrium problems in real Hilbert spaces. We replace the second minimization problem onto a closed convex set in the extragradient method, with a subgradient projection onto some constructible half-space and propose a new method of getting the step-size. A convergence theorem for the generated sequence is proved and applied for finding a solution of variational inequality problem.

KEYWORDS:

• Subgradient extragradient method
• pseudo-monotone equilibrium problems
• weak convergence
• Hilbert spaces

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H06
• 47H09
• 47J05
• 47J25

Disclosure statement

No potential conflict of interest was reported by the authors.