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求鞍点问题的新的原始-对偶算法

张纯, 蔡邢菊, 韩德仁   

  1. 南京师范大学数学科学学院, 南京 210023
  • 收稿日期:2016-01-31 出版日期:2016-09-15 发布日期:2016-09-08

张纯, 蔡邢菊, 韩德仁. 求鞍点问题的新的原始-对偶算法[J]. 数值计算与计算机应用, 2016, 37(3): 167-178.

Zhang Chun, Cai Xingju, Han Deren. A NEW PRIMAL-DUAL ALGORITHM FOR SOLVING SADDLE-POINT PROBLEMS[J]. Journal of Numerical Methods and Computer Applications, 2016, 37(3): 167-178.

A NEW PRIMAL-DUAL ALGORITHM FOR SOLVING SADDLE-POINT PROBLEMS

Zhang Chun, Cai Xingju, Han Deren   

  1. School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China
  • Received:2016-01-31 Online:2016-09-15 Published:2016-09-08
本文考虑求解鞍点问题的原始-对偶算法.通过对算法中的子问题加以修正,得到一类新的原始-对偶算法.在适当的假设条件下,证明了算法的收敛性.同时,将算法应用到一些图像处理问题,并与其它的原始-对偶类算法进行数值比较.结果表明,新的算法更加有效.
The primal-dual hybrid gradient algorithm for solving saddle-point problems is very popular in recent years, due to its simplicity and efficiency in dealing with problems especially those arising from image processing. In this paper, we propose a modified primal-dual hybrid gradient algorithm, where in the primal and dual steps, we first move along the gradient direction, and then solve the same proximal subproblems to generate the next iteration. Under suitable conditions, we prove the global convergence of the algorithm. We also report some preliminary numerical results and compare it with some state-of-the-art primal-dual gradient algorithms, showing the competitiveness of the new algorithm.

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