A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces

Jean Strodiot (), Phan Vuong () and Thi Nguyen ()

Journal of Global Optimization, 2016, vol. 64, issue 1, 159-178

Abstract: A new class of extragradient-type methods is introduced for solving an equilibrium problem in a real Hilbert space without any monotonicity assumption on the equilibrium function. The strategy is to replace the second projection step in the classical extragradient method by a projection onto shrinking convex subsets of the feasible set. Furthermore, to ensure a sufficient decrease on the equilibrium function, a general Armijo-type condition is imposed. This condition is shown to be satisfied for four different linesearches used in the literature. Then, the weak and strong convergence of the resulting algorithms is obtained under non-monotonicity assumptions. Finally, some numerical experiments are reported. Copyright Springer Science+Business Media New York 2016

Keywords: Non-monotone equilibrium problems; Shrinking projection methods; Extragradient methods; Weak convergence; Strong convergence (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-015-0365-5

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