非凸两分块问题乘子交替方向法的收敛性分析

摘要

The Alternating Direction Method of Multipliers(ADMM)is an effective method for large scale optimization problems.While the convergence of ADMM has been clearly recognized in the case of convex,the convergence result of ADMM in the case of nonconvex is still an open problem.In this paper,under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Loj asiewicz inequality and the penalty parameter is greater than a constant,we an-alyze the convergence of ADMM for a class of nonconvex optimization problems whose obj ec-tive function is the sum of two block nonconvex functions.%乘子交替方向法(ADMM)求解大规模问题十分有效.ADMM在凸情形下的收敛性已被清晰认识，但非凸问题 ADMM的收敛性结果还很少.本文针对非凸两分块优化问题，在增广拉格朗日函数满足 Kurdyka-Loj as-iewicz不等式性质且罚参数大于某个常数的条件下，证明了 ADMM的收敛性.