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

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▽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.

Approximate inexact accelerated proximal gradient method for the minimization problem of a class of maximum eigenvalue functions

Inexact accelerated proximal gradient method has already been used to solve the problem min{F（X） = f（X） ＋ g（X） ： X∈ S^n }. 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.