Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization

Ju, Jiangwen; Lin, Weixin; Liu, Hao

doi:10.3390/math14101750

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Open AccessArticle

Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization

by

Jiangwen Ju

,

Weixin Lin

^*

and

Hao Liu

^*

School of Mathematical and Physical Sciences, Nanjing Tech University, Nanjing 211816, China

^*

Authors to whom correspondence should be addressed.

Mathematics 2026, 14(10), 1750; https://doi.org/10.3390/math14101750

Submission received: 13 April 2026 / Revised: 12 May 2026 / Accepted: 16 May 2026 / Published: 19 May 2026

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

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Abstract

We extend the modified BFGS algorithm to a limited-memory framework, and propose a self-adaptive limited-memory quasi-Newton method, denoted as LADBFGS, for large-scale unconstrained optimization. The proposed method fully exploits function value information to improve the curvature approximation of the objective function, while enabling dynamic and adaptive adjustment of parameters. We establish the global R-linear convergence of the proposed algorithm for uniformly convex problems. Numerical experiments on 102 standard unconstrained test functions with dimensions of no less than 1000 show that the proposed LADBFGS method outperforms the standard limited-memory BFGS method in terms of iteration count, number of function and gradient evaluations, and computational time, and also achieves a higher success rate for solving the test problems.

Keywords: unconstrained optimization; quasi-Newton method; limited-memory BFGS; weak secant equation

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MDPI and ACS Style

Ju, J.; Lin, W.; Liu, H. Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization. Mathematics 2026, 14, 1750. https://doi.org/10.3390/math14101750

AMA Style

Ju J, Lin W, Liu H. Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization. Mathematics. 2026; 14(10):1750. https://doi.org/10.3390/math14101750

Chicago/Turabian Style

Ju, Jiangwen, Weixin Lin, and Hao Liu. 2026. "Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization" Mathematics 14, no. 10: 1750. https://doi.org/10.3390/math14101750

APA Style

Ju, J., Lin, W., & Liu, H. (2026). Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization. Mathematics, 14(10), 1750. https://doi.org/10.3390/math14101750

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Self-Adaptive Limited-Memory Quasi-Newton Method with Function Value Information for Large-Scale Unconstrained Optimization

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