A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces

Gang Cai (), Aviv Gibali (), Olaniyi S. Iyiola () and Yekini Shehu ()
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Gang Cai: Chongqing Normal University
Aviv Gibali: ORT Braude College
Olaniyi S. Iyiola: University of Wisconsin-Milwaukee
Yekini Shehu: University of Nigeria

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 1, No 11, 219-239

Abstract: Abstract In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under mild and standard assumptions, we establish the strong convergence of our algorithm in a uniformly smooth and convex Banach spaces. We also present a modification of our method using a line-search approach, this enable to obtain strong convergence in real and reflexive Banach spaces, without the prior knowledge of the Lipschitz constant. Numerical experiments illustrate the performances of our new algorithm and provide a comparison with related algorithms. Our results generalize and extend some of the existing works in Hilbert spaces to Banach spaces as well as provide an extension from weak to strong convergence.

Keywords: Variational inequality problem; Halpern method; Strong convergence; Subgradient extragradient method; Line-search; 47H05; 47J20; 47J25; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1228-2

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