Extragradient Methods and Linesearch Algorithms for Solving Ky Fan Inequalities and Fixed Point Problems

Phan Tu Vuong (), Jean Jacques Strodiot () and Nguyen Van Hien ()
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Phan Tu Vuong: Institute for Computational Science and Technology at Ho Chi Minh City (ICST HCMC)
Jean Jacques Strodiot: Institute for Computational Science and Technology at Ho Chi Minh City (ICST HCMC)
Nguyen Van Hien: Institute for Computational Science and Technology at Ho Chi Minh City (ICST HCMC)

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 2, No 14, 605-627

Abstract: Abstract In this paper, we introduce some new iterative methods for finding a common element of the set of points satisfying a Ky Fan inequality, and the set of fixed points of a contraction mapping in a Hilbert space. The strong convergence of the iterates generated by each method is obtained thanks to a hybrid projection method, under the assumptions that the fixed-point mapping is a ξ-strict pseudocontraction, and the function associated with the Ky Fan inequality is pseudomonotone and weakly continuous. A Lipschitz-type condition is assumed to hold on this function when the basic iteration comes from the extragradient method. This assumption is unnecessary when an Armijo backtracking linesearch is incorporated in the extragradient method. The particular case of variational inequality problems is examined in a last section.

Keywords: Ky Fan’s inequality; Fixed-point problem; Hybrid projection method; Extragradient method; ξ-Strict pseudocontraction; Armijo backtracking linesearch; Lipschitz continuity (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10957-012-0085-7

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