A Predictor-Corrector Method for Solving Equilibrium Problems
We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new p...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/313217 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850216629694103552 |
|---|---|
| author | Zong-Ke Bao Ming Huang Xi-Qiang Xia |
| author_facet | Zong-Ke Bao Ming Huang Xi-Qiang Xia |
| author_sort | Zong-Ke Bao |
| collection | DOAJ |
| description | We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise to Δ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities. |
| format | Article |
| id | doaj-art-366d2c9d47014ee5b94ffd574cfc666b |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-366d2c9d47014ee5b94ffd574cfc666b2025-08-20T02:08:15ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/313217313217A Predictor-Corrector Method for Solving Equilibrium ProblemsZong-Ke Bao0Ming Huang1Xi-Qiang Xia2School of Accounting, Zhejiang University of Finance and Economics, Hangzhou 310018, ChinaDalian University of Technology, Dalian 116024, ChinaDalian University of Technology, Dalian 116024, ChinaWe suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise to Δ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.http://dx.doi.org/10.1155/2014/313217 |
| spellingShingle | Zong-Ke Bao Ming Huang Xi-Qiang Xia A Predictor-Corrector Method for Solving Equilibrium Problems Abstract and Applied Analysis |
| title | A Predictor-Corrector Method for Solving Equilibrium Problems |
| title_full | A Predictor-Corrector Method for Solving Equilibrium Problems |
| title_fullStr | A Predictor-Corrector Method for Solving Equilibrium Problems |
| title_full_unstemmed | A Predictor-Corrector Method for Solving Equilibrium Problems |
| title_short | A Predictor-Corrector Method for Solving Equilibrium Problems |
| title_sort | predictor corrector method for solving equilibrium problems |
| url | http://dx.doi.org/10.1155/2014/313217 |
| work_keys_str_mv | AT zongkebao apredictorcorrectormethodforsolvingequilibriumproblems AT minghuang apredictorcorrectormethodforsolvingequilibriumproblems AT xiqiangxia apredictorcorrectormethodforsolvingequilibriumproblems AT zongkebao predictorcorrectormethodforsolvingequilibriumproblems AT minghuang predictorcorrectormethodforsolvingequilibriumproblems AT xiqiangxia predictorcorrectormethodforsolvingequilibriumproblems |