近似非精确加速迫近梯度方法求解一类最大特征值函数极小化问题

摘要

Inexact accelerated proximal gradient method has already been used to solve the problem min{F(X) = f (X) + g(X) :X∈ Sn} .The function f :Sn→ R is continuously differentiable and its gradient ▽f is Lipschitz continuous ,functions f and g are all proper ,lower semi-continuous convex functions(possibly non-smooth) .Considering the approximate IAPG method ,with the help of the smooth approximation to the non-smooth function ,we solve the minimization problem of the sum of maximum eigenvalue function and general non-smooth function g(X) .Then the AIAPG method can be obtained and the convergence can be proved .The AIAPG method was used to solve the minimiza-tion of the maximum eigenvalue function with linear constraint .%非精确加速迫近梯度（IAPG）算法，用于解决问题min｛F（X）＝f（X）＋g（X）：X∈Sn｝，其中函数f：Sn→R是连续可微的，且楚f是Lipschitz连续的，函数f，g均是正常的，下半连续凸函数（可能非光滑）。利用近似IAPG算法借助于非光滑函数的光滑近似，解决非光滑函数中最大特征值函数与一般非光滑函数g（x）的和的极小化问题，得出近似IAPG算法，并给出了收敛性分析。将近似IAPG算法用于求解带有线性约束的最大特征值函数的优化问题。