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

Numerical Analysis 2022-04-19 v1 Numerical Analysis

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.

Keywords

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

R2 v1 2026-06-24T10:50:10.935Z