%0 Journal Article
%T 求解非凸优化问题的带惯性项Majorized Bregman交替方向乘子法<br>Majorized Bregman Alternating Direction Method of Multipliers with Inertia Terms for Solving Nonconvex Optimisation Problems
%A 吴展雄
%A 陆莎
%A 黄清梅
%J Advances in Applied Mathematics
%P 119-134
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.146306
%X 对非凸两分块优化问题&#65292;提出一种带惯性的Majorized Bregman交替方向乘子法。该算法在迭代中结合了目标函数的极大化线性技术和Bregman距离来简化子问题的求解&#65292;同时通过引入惯性项加快收敛效果。在适当条件下证明了算法的收敛性质。初步数值实验结果表明该算法是有效的。<br>A Majorized Bregman alternating direction method of multipliers (Bregman-ADMM) with inertial terms is proposed for nonconvex two-block optimization problems. The algorithm combines a linearization technique for the objective function and the Bregman distance in each iteration to simplify subproblem solutions, while accelerating the convergence rate through inertial terms. The convergence of the algorithm is established under appropriate conditions. Preliminary numerical experiments demonstrate the effectiveness of the proposed algorithm.
%K 交替方向乘子法&#65292
%K Bregman距离&#65292
%K 惯性项&#65292
%K KL性质<br>Alternating Direction Method of Multipliers
%K Bregman Distance
%K Inertial Term
%K Kurdyka-&#321
%K ojasiewicz Property
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=117409