Solving strongly monotone variational and quasi-variational inequalities

Iterative methods for solving monotone equilibrium problems via dual gap functions

“…This method is known as an extrapolation from the extragradient algorithm or a double projection-type method. In this section, we extend the idea in [15] to strongly monotone equilibrium problems that satisfy a certain Lipschitz-type condition. We prove the global convergence of the proposed algorithm and estimate its complexity.…”

“…Recently, Nesterov and Scrimali [15] proposed an iterative method for solving strongly monotone variational inequalities that satisfy a Lipschitz condition. This method is known as an extrapolation from the extragradient algorithm or a double projection-type method.…”

“…Other solution methods have been well developed in mathematical programming and variational inequalities such as gap function-based, extragradient and bundle methods [5,[14][15][16] recently have been extended to equilibrium problems [13,19,22].…”

“…In this paper, we first extend the method proposed in [15] for strongly monotone variational inequalities to strongly monotone equilibrium problems that satisfy a certain Lipschitz-type condition. The global convergence of the proposed algorithm is investigated and the complexity is estimated.…”

Gap functions and error bounds for quasi variational inequalities

“…The QV I P and its other variants have received considerable attention in recent years from theoretical viewpoint, applications and solutions methodologies. We may address the readers to few papers [4,14,15,18,20,21].…”