New inertial algorithm for a class of equilibrium problems
The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with inertial effects. The main novelty of the algorithm is that it...
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| Published in | Numerical algorithms Vol. 80; no. 4; pp. 1413 - 1436 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.04.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-018-0532-0 |
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| Abstract | The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with inertial effects. The main novelty of the algorithm is that it can be done without previously knowing the information on the strongly pseudomonotone and Lipschitz-type constants of cost bifunction. A reasonable explain for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. Theorem of strong convergence is proved. In the case, when the information on the modulus of strong pseudomonotonicity and Lipschitz-type constant is known, the rate of linear convergence of the algorithm has been established. Several of experiments are performed to illustrate the numerical behavior of the algorithm and also compare it with other algorithms. |
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| AbstractList | The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with inertial effects. The main novelty of the algorithm is that it can be done without previously knowing the information on the strongly pseudomonotone and Lipschitz-type constants of cost bifunction. A reasonable explain for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. Theorem of strong convergence is proved. In the case, when the information on the modulus of strong pseudomonotonicity and Lipschitz-type constant is known, the rate of linear convergence of the algorithm has been established. Several of experiments are performed to illustrate the numerical behavior of the algorithm and also compare it with other algorithms. |
| Author | Van Hieu, Dang |
| Author_xml | – sequence: 1 givenname: Dang surname: Van Hieu fullname: Van Hieu, Dang email: dangvanhieu@tdt.edu.vn organization: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University |
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| Keywords | Proximal-like method Strongly pseudomonotone bifunction 47J20 Equilibrium problem Lipschitz-type bifunction 47H05 47J25 Regularized method 65J15 91B50 |
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