高阶优化算法分析简介

高阶优化算法是利用目标函数的高阶导数信息进行优化的算法,是最优化领域中的一个新兴的研究方向.高阶算法具有更低的迭代复杂度,但是需要求解一个更难的子问题.主要介绍三种高阶算法,分别为求解凸问题的高阶加速张量算法和A-HPE框架下的最优张量算法,以及求解非凸问题的ARp算法.同时也介绍了怎样求解高阶算法的子问题.希望通过对高阶算法的介绍,引起更多学者的关注与重视.

Introduction to high-order optimization methods

High-order methods are the recently developed optimization algorithms of using high-order information in the process of iteration. The high-order methods often have lower iteration complexity yet a harder subproblem to solve comparing to first-order methods. In this paper, we mainly surveyed three high-order methods including accelerated tensor method, the optimal tensor method, and the ARp method. The solution methods of the subproblems associated with those methods are discussed as well. Hopefully, the interested readers will pay more attention to this research topic by reading the recent advances of high-order methods summarized in this paper.