求解可分离凸优化问题的惯性近似松弛交替方向乘子法

Inertia approximate relaxation alternating direction multiplier method for separable convex optimization problems

基于交替方向乘子法(ADMM)提出了一种求解可分离凸优化可行问题的惯性近似松弛交替方向乘子法(IPR-ADMM)。新构造的算法不仅具有提高算法收敛性的优势的惯性外推项,而且引入随机变量以随机加速新步长,从而提高算法的灵活性。并在适当的假设下,证明了算法的全局迭代收敛性。数值实验结果表明,数据维数取值越大,算法收敛越快,越趋于稳定,且IPRADMM算法的收敛性明显优于扩展的邻近交替方向法(ePADM)。

Based on alternating direction multiplier method(ADMM),an inertial approximate relaxation alternating direction multiplier method(IPR-ADMM)was proposed to solve separable convex optimization feasible problems.The new algorithm not only integrated the advantages of inertia extrapolation term to improve the convergence of the algorithm,but also introduced random variables to accelerate the new step size randomly,so as to improve the flexibility of the algorithm.Under suitable assumptions,the global convergence of the algorithm was proved.The numerical results show that the larger the data dimension is,the faster and more stable the convergence of the algorithm is.Moreover,the convergence of IPR-ADMM algorithm is better than that of ePADM algorithm.