邻近次梯度法求解弱凸问题的收敛率分析

On the Convergence Rate of Proximal Subgradient Algorithm for Weakly Convex Problems

邻近次梯度算法是求解两个凸函数和的经典方法 .本文对凸问题的目标函数做了适当的推广,在有限维欧几里得空间中,提出了利用邻近次梯度算法求解弱凸函数与凸函数和的优化问题,在目标函数具有尖性的假设下,证明了取Polyak步长时算法线性收敛.本文得到的结果,是对Cruz和Davis等人结果的推广.

The proximal subgradient algorithm is a classical method to solve the sum of two convex functions. In this paper, the objective functions of convex problems are appropriately generalized. It also proposes the optimization problem of solving the sum of weakly convex functions and convex functions by using the proximal subgradient algorithm. Under the assumption that the objective functions have sharpness, the linear convergence of the algorithm with Polyak step