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N.T.T. Van, J. Strodiot, V.H. Nguyen, V. Phan:
"An extragradient-type method for solving nonmonotone quasi-equilibrium problems";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2017-12 (2017), 21 pages.

In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.

Extragradient-type method, quasi-equilibrium problem, nonmonotone operator, convergence

http://publik.tuwien.ac.at/files/publik_265352.pdf