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

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.