Efficient iterative method for SOAV minimization problem with linear equality and box constraints and its linear convergence
Efficient iterative method for SOAV minimization problem with linear equality and box constraints and its linear convergence
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DOI：
10.1016/j.jfranklin.2022.01.014
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发表时间：
2022-02
期刊：
影响因子：
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通讯作者：
Mitsuru Toyoda;Mirai Tanaka
中科院分区：
文献类型：
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作者：
Mitsuru Toyoda;Mirai Tanaka
利用乘子交替方向法(ADMM)，提出了一种求解具有线性等式和盒子约束的绝对值和(SOAV)最小化问题的高效算法。在ADMM的迭代中，采用了高效的邻近点计算算法，这是子问题的解，对计算效率有很大的影响。通过分析迭代的动力学结构，证明了该算法的线性收敛性质。最后，通过机械系统离散控制的实际应用，说明了该方法的优越性。
This study proposes an efficient algorithm for the sum-of-absolute-values (SOAV) minimization problem with linear equality and box constraints by exploiting alternating direction method of multipliers (ADMM). In the iteration of ADMM, efficient algorithms for the calculations of proximal points, which are the solutions of sub-problems and have great effects on the computation efficiency, are employed. By focusing on the dynamical structure of the iteration, the linear convergence of the proposed algorithm is proven. Furthermore, a practical application for mechanical system control with discrete-valued control illustrates the advantages of the proposed methods.