A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization

Jiawei Chen (), Yushan Bai (), Guolin Yu (), Xiaoqing Ou () and Xiaolong Qin ()
Additional contact information
Jiawei Chen: Southwest University
Yushan Bai: Southwest University
Guolin Yu: North Minzu University
Xiaoqing Ou: North Minzu University
Xiaolong Qin: Hangzhou Normal University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 1, No 13, 30 pages

Abstract: Abstract A novel Polak-Ribière-Polyak (PRP) type conjugate gradient method is proposed to solve a nonconvex vector optimization. This variant is a nontrivial extension of a PRP type conjugate gradient method from the scalar case to the vector case. We construct a new nonnegative conjugate parameter avoiding the usual truncation of conjugate gradient method. The search direction in the new PRP type conjugate gradient method is proved to satisfy the sufficient descent condition without involving any line search. The globally convergent results of the novel conjugate gradient method are derived under the standard Wolfe line search as well as the Armijo line search strategy without convexity assumption of the objective functions. Besides, the iterative sequence generated by the proposed method is also proved to be weakly convergent to some weak Pareto optimal solution of the vector optimization problem under the cone-pseudoconvexity assumption. Numerical experiments also manifest the validity of the proposed novel method. The gained results improve the corresponding results of (SIAM J Optim 28:2690–2720, 2018 and Comput Optim Appl 86:457–489, 2023).

Keywords: Vector optimization; Pareto critical point; Conjugate gradient method; Global convergence; Robust function; 90C30; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02571-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02571-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-024-02571-7

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().