A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient
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 \beta_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.
Cite
@article{arxiv.2204.07930,
title = {A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient},
author = {Bingjie Li and Tianhao Ni and Zhenyue Zhang},
journal= {arXiv preprint arXiv:2204.07930},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2102.08048