自适应步长带回代的邻近分块乘子极小化算法

Proximal Block Multiplier Minimization Algorithm with Adaptive Step Size and Substitution Procedure

本文考虑求解带线性约束的多块凸优化问题,其中的目标函数有一项不可分离。对于目标函数中存在不可分离项,晁绵涛等人将块坐标下降法与交替方向乘子法相结合提出了PBMM-MS算法,并通过数值实验验证了其有效性。本文对PBMM-MS算法进行改进,提出了自适应步长带回代的邻近分块乘子极小化算法,该算法结合了步长的自适应调整技术,使步长在迭代过程中自动调整,提高了算法的计算效率。对于提出的算法,我们证明了其收敛性。

This paper talks about solving multi-block convex optimization problems with linear constraints,among which is the inseparable term of object function.To solve the problem,Chao miautao et al.hewe proposed a PBMM-MS algorithm by integrating block coordinate descent method with alternating direction method of multipliers,and verified its validity via numerical experiments.Based on PBMM-MS algorithm,a new algorithm with adaptive step size and substitution procedure is proposed.The algorithm adopts the adaptive step size technique that enables automatical adjustment of the step size during the iterative process.Hence,the computational efficiency of the algorithm is improved.In addition,global convergence of the proposed algorithm is also derived.