%0 Journal Article
%T 带有绝对值形式的非线性约束下的交替方向乘子法<br>Alternating Direction Method of Multipliers under Nonlinear Constraints with Absolute Value Form
%A 叶景然
%A 陈跨越
%A 杨硕
%A 苏映梅
%J Advances in Applied Mathematics
%P 382-397
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.143126
%X 交替方向乘子法(Alternating Direction Method of Multipliers, ADMM)广泛应用于线性约束优化问题&#65292;无论是凸目标函数还是非凸目标函数&#65292;其约束一般是线性约束。文章研究了具有绝对值形式的非线性约束的非凸极小化问题的ADMM。在假设相关函数满足Kurdyka-Lojasiewicz (KL)不等式的情况下&#65292;证明了由ADMM生成的迭代子序列收敛于问题的一个临界点&#65292;并根据一些数值例子说明了ADMM是可行的。<br>The Alternating Direction Method of Multipliers (ADMM) is widely used for linear constraint optimization problems, whether the objective function is convex or non-convex, with constraints generally being linear. This article studies the ADMM applied to non-convex minimization problems with nonlinear constraints in the form of absolute values. Under the assumption that the relevant functions satisfy the Kurdyka-Lojasiewicz (KL) inequality, it is proved that the iterative subsequence generated by ADMM converges to a critical point of the problem. Additionally, some numerical examples are provided to illustrate the feasibility of ADMM.
%K 交替方向乘子法&#65292
%K 非线性约束&#65292
%K 绝对值&#65292
%K 收敛性<br>Alternating Direction Method of Multipliers
%K Nonlinear Constraints
%K Absolute Value
%K Convergence
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=110147