求解逻辑回归问题的多层邻近拟牛顿算法  

An multi-level proximal quasi-Newton algorithm for solving logistic regression problems

作　　者：肖斌 周芷娟 胡清洁[1] XIAO Bin;ZHOU Zhijuan;HU Qingjie(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2022年第2期133-137,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11961011,11761014)。

摘　　要：针对逻辑回归问题,基于多层优化思想和邻近拟牛顿算法,提出一种求解该问题的多层邻近拟牛顿算法。先构造粗糙模型,再根据粗糙条件判断选择执行粗糙步或邻近拟牛顿步。此外,为节省计算量,该算法给出一个合理的目标函数二阶近似,并近似求解子问题。数值结果表明,该算法在求解逻辑回归问题时是有效的。Aiming at the logistic regression problem,based on the idea of multi-level optimization and proximal quasi-Newton algorithm,a multi-level proximal quasi-Newton algorithm is proposed to solve this problem.The algorithm first constructs a coarse model,and then the algorithm executes the coarse steps or proximal quasi-Newton steps through the coarse conditions.And in order to save the computations costs,the algorithm gives a reasonable second-order approximation to the objective function and solves the sub-problems approximately.The final numerical results show that the algorithm is effective in solving the logistic regression problems.

关 键 词：凸优化 逻辑回归问题 多层优化 邻近拟牛顿算法 非精确 

分 类 号：O224[理学—运筹学与控制论]