Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and simplest one. Due to slow convergence rate of Newton's methods, many research have been carried out to modify the Newton's method for faster convergence rate. In 2019, Ghazali et al. modified Newton's method and proposed Netwon-SOR method, which is a combination of Newton method with SOR iterative method to solve a linear system. In this paper, we propose a modification of Newton-SOR method by modifying SOR method to generalized SOR method. Numerical experiments are carried out to check the efficiently of the proposed method.

翻译：无约束凸优化问题在科学与工程的各个领域具有广泛应用。现有文献中存在多种迭代方法可求解此类问题，其中牛顿法是最古老且最简单的方法之一。由于牛顿法收敛速度较慢，学界已开展大量研究对其进行改进以提升收敛速率。2019年，Ghazali等人通过将牛顿法与SOR迭代法相结合以求解线性系统，提出了牛顿-SOR方法。本文对牛顿-SOR方法进行改进，将SOR方法推广为广义SOR方法。通过数值实验验证了所提方法的有效性。