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Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space

Nguyen Minh Khoa|Tran Van Thang
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회보 (Bulletin of the KMS)|제59권 제4호|pp. 1019-1044|DOI 10.4134/BKMS.b210607

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참고문헌

키워드

Equilibrium problempseudomonotonemultivalued variational inequality problemsubgradientapproximate projectionTseng's extragradient method
주제분류수학

초록

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

Abstract

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

참고문헌 (30)

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관련 논문AI추천

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