| 一种带有不定性邻近项的广义Peaceman-Rachford分裂法 |
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| 引用本文： | 马,龙,彭建文.一种带有不定性邻近项的广义Peaceman-Rachford分裂法[J].应用数学,2020,33(2):423-435. |
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| 作者姓名： | 马 龙 彭建文 |
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| 作者单位： | 重庆师范大学数学科学学院, 重庆 401331 |
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| 基金项目： | 重庆市基础科学与前沿技术研究(重点)(NO.cstc2015jcyjBX0029);国家自然科学基金面上项目(11171363)。 |
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| 摘 要： | 针对带有线性约束的可分离凸优化问题,提出一种带有不定邻近项的广义Peaceman-Rachford(PR)分裂法.在较弱假设条件下,证明该算法迭代序列的全局收敛性和建立起在遍历情况下的最坏O(1/t)收敛速率.最后,通过数值实验验证了所提算法的有效性.
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| 关 键 词： | 凸优化 Peaceman-Rachford分裂法 不定邻近项 |
| 收稿时间： | 2019/4/10 0:00:00 |
A Generalized Peaceman-Rachford Splitting Method with Indefinite Proximal Term |
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| MA Long,PENG Jianwen.A Generalized Peaceman-Rachford Splitting Method with Indefinite Proximal Term[J].Mathematica Applicata,2020,33(2):423-435. |
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| Authors: | MA Long PENG Jianwen |
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| Institution: | (School of Mathematics Sciences,Chongqing Normal University,Chongqing 401331,China) |
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| Abstract: | To deal with the separable convex optimization problems with linear constraints,a generalized Peaceman-Rachford(PR)splitting method with indefinite proximal term is proposed.Under certain weak assumptions,the global convergence of the iterative sequence generated by the proposed algorithm is proved,and the worst-case O(1/t)convergence rate in the ergodic sense is established.Finally,the effectiveness of the proposed algorithm is proved in numerical experiments. |
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| Keywords: | Convex optimization Peaceman-Rachford split method Indefinite proximal term |
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