Reference : Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and f...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and fixed point problems
Phan, Vuong mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Jean Jacques, Strodiot mailto [Facultés Universitaires Notre-Dame de la Paix - Namur - FUNDP > Mathematics]
Nguyen, Van Hien mailto [Facultés Universitaires Notre-Dame de la Paix - Namur - FUNDP]
Journal of Optimization Theory and Applications
Springer Science & Business Media B.V.
Yes (verified by ORBilu)
[en] Ky Fan’s inequality Fixed-point problem Hybrid projection method Extragradient method ξ-Strict pseudocontraction Armijo backtracking linesearch Lipschitz continuity
[en] 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.

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