“…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.…”
Section: Algorithm For Strongly Monotone Equilibrium Problemsmentioning
confidence: 99%
“…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.…”
Section: Algorithm For Strongly Monotone Equilibrium Problemsmentioning
confidence: 99%
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of linear equilibrium problems is investigated and numerical examples are implemented to verify our algorithms.
“…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.…”
Section: Algorithm For Strongly Monotone Equilibrium Problemsmentioning
confidence: 99%
“…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.…”
Section: Algorithm For Strongly Monotone Equilibrium Problemsmentioning
confidence: 99%
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of linear equilibrium problems is investigated and numerical examples are implemented to verify our algorithms.
“…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].…”
The paper aims to obtain new local/global error bounds for quasi variational inequality problems in terms of the regularized gap function and the D-gap function. These bounds provide effective estimated distances between a specific point and the exact solution of quasi variational inequality problem.
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