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

Strodiot, Jean Jacques, Vuong, Phan Tu and Nguyen, Thi Thu Van (2016) A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces. Journal of Global Optimization, 64 (1), 159-178. (doi:10.1007/s10898-015-0365-5).

Record type: Article

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.

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