中文摘要：

讨论了一类非光滑凸优化的空间分解方法,其目标函数是分片二次连续可微的凸函数.首先给出该优化的空间分解;然后给出优化问题的U-拉格朗日函数及其一阶、二阶性质;最后给出该优化的具有超线性收敛速度的分解算法,并证明了算法的收敛性.

英文摘要：

The space decomposition method for a class of nonsmooth convex optimization problems is discussed.The objective function is piecewise twice continuous differentiable function,which has the connection with space decomposition.Firstly,the space decomposition is given.Secondly,the ULagrangian function and its first and second-order properties are discussed.At last,an algorithm with superlinear convergence rate is proposed and this method is proved to be converged.