非线性优化问题中的共轭梯度法研究综述

Review of Conjugate Gradient Method in Nonlinear Optimization Problems

共轭梯度法是解决大规模线性等式和非线性优化问题的重要方法之一,其突出优点是收敛性强、迭代步骤简单、对存储要求低.因此,通过查阅大量国内外文献,介绍几种经典共轭梯度法及其改进算法的发展趋势和收敛性,并阐述混合共轭梯度法的研究热点以及共轭梯度法在图像复原和压缩感知中的应用,同时探讨了现有算法的局限性及其未来的研究方向.

Conjugate gradient method is one of the important methods to solve large linear equation and nonlinear optimization problems.Its outstanding advantages are strong convergence,simple iterative steps and low storage requirements.Therefore,through the study of extensive domestic and foreign literature,we introduced several classical Conjugate gradient methods and the developing trend of its improving algorithm and convergence;stated the research focus of mixed conjugate gradient method and the application of conjugate gradient method in image restoration and compressed sensing.At the same time,the shortcoming of existing algorithms and possible research directions in the future were given.