A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient

2022/04/17 by Li, Bingjie, Ni, Tianhao, Zhang, Zhenyue
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2204.07930

Abstract

In this paper, we propose a modified nonlinear conjugate gradient (NCG) method for functions with a non-Lipschitz continuous gradient. First, we present a new formula for the conjugate coefficient β_k in NCG, conducting a search direction that provides an adequate function decrease. We can derive that our NCG algorithm guarantees strongly convergent for continuous differential functions without Lipschitz continuous gradient. Second, we present a simple interpolation approach that could automatically achieve shrinkage, generating a step length satisfying the standard Wolfe conditions in each step. Our framework considerably broadens the applicability of NCG and preserves the superior numerical performance of the PRP-type methods.

Related

• A nonlinear conjugate gradient method with complexity guarantees and its application to nonconvex regression
• Algorithm 851
• Nonlinear conjugate gradient methods: worst-case convergence rates via computer-assisted analyses
• Modified parameter of Dai Liao conjugacy condition of the conjugate gradient method
• Nonlinear conjugate gradient for smooth convex functions