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Weak and strong convergence of subgradient extragradient methods for pseudomonotone equilibrium problems

Dang Van Hieu
대한수학회 (The Korean Mathematical Society)|2016.10|대한수학회논문집 (Communications of the KMS)|제31권 제4호|pp. 879-893

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참고문헌

키워드

hybrid methodequilibrium problemsubgradient methodextragradient method
주제분류수학

초록

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

Abstract

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

참고문헌 (29)

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관련 논문AI추천

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