New Explicit Extragradient Methods for Solving a Class of Bilevel Equilibrium Problems

The paper proposes a new explicit extragradient algorithm for solving an equilibrium problem over the solution set of another generalized equilibrium problem which usually is called bilevel equilibrium problems in a real Hilbert space. The algorithm combines extragradient methods with auxiliary problem techniques. Theorem of the strong convergence of the algorithm is established under standard assumptions imposed on the cost bifunctions. Finally, several of fundamental experiments are provided to illustrate the numerical behavior of the algorithm and also to compare with others.