运筹学学报 >
2023 , Vol. 27 >Issue 3: 37 - 52
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.003
非凸两分块优化问题的一类惯性对称正则化交替方向乘子法
收稿日期: 2021-04-21
网络出版日期: 2023-09-14
基金资助
国家自然科学基金重大项目(11991024);国家自然科学基金面上项目(12271071);重庆英才·创新创业领军人才·创新创业示范团队项目(CQYC20210309536);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金(cstc2021jcyj-msxmX0300)
A class of inertial symmetric regularization alternating direction method of multipliers for nonconvex two-block optimization
Received date: 2021-04-21
Online published: 2023-09-14
交替方向乘子法(ADMM)是一个求解可分离凸优化问题的的有效方法，然而，当目标函数存在非凸函数时，ADMM或许不收敛。本文提出一类带线性等式约束的非凸两分块优化问题的惯性对称正则化交替方向乘子法。在适当的假设条件下，建立了算法的全局收敛性。其次，在效益函数满足Kurdyka-Łojasiewicz (KL)性质时，建立了算法的强收敛性。最后，对算法进行了数值实验，结果说明算法是一种有效的方法。
关键词： 交替方向乘子法; 非凸优化问题; Kurdyka-Łojasiewicz (KL)性质; 收敛性
彭建文, 雷宏旺 . 非凸两分块优化问题的一类惯性对称正则化交替方向乘子法[J]. 运筹学学报, 2023 , 27(3) : 37 -52 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.003
The alternating direction method of multipliers(ADMM) is an valid method for solving separable convex optimization problems, nevertheless, when the objective function has a nonconvex function, ADMM may not converge. This paper proposes an inertial symmetric regularization alternating direction method of multipliers for nonconvex two-block optimization problem with linear equality constraints. Under the appropriate hypothesis conditions, the global convergence of the algorithm is established. Secondly, When the benefit function satisfies the Kurdyka-Łojasiewicz(KL) property, the strong convergence of the algorithm is established. Finally, numerical experiments are performed on the algorithm, and the results show that the algorithm is an effective method.
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