A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations

作者：Yuan, Gonglin^*; Meng, Zehong; Li, Yong

来源：Journal of Optimization Theory and Applications, 2016, 168(1): 129-152.

DOI：10.1007/s10957-015-0781-1

• Nonsmooth
• Nonlinear equations
• Conjugate gradient
• Large scale
• Global convergence

It is well known that nonlinear conjugate gradient methods are very effective for large-scale smooth optimization problems. However, their efficiency has not been widely investigated for large-scale nonsmooth problems, which are often found in practice. This paper proposes a modified Hestenes-Stiefel conjugate gradient algorithm for nonsmooth convex optimization problems. The search direction of the proposed method not only possesses the sufficient descent property but also belongs to a trust region. Under suitable conditions, the global convergence of the presented algorithm is established. The numerical results show that this method can successfully be used to solve large-scale nonsmooth problems with convex and nonconvex properties (with a maximum dimension of 60,000). Furthermore, we study the modified Hestenes-Stiefel method as a solution method for large-scale nonlinear equations and establish its global convergence. Finally, the numerical results for nonlinear equations are verified, with a maximum dimension of 100,000.

• 出版日期2016-1
• 单位浙江财经大学; 百色学院; 广西大学