A Novel Hybrid Conjugate Gradient Algorithm for Solving Unconstrained Optimization Problems

Authors

  • Romaissa Mellal Laboratory of Analysis and Control of Differential Equations, Department of Mathematics, 8th May 1945 University, Guelma, Algeria
  • Nabil Sellami Laboratory of Analysis and Control of Differential Equations, Department of Mathematics, 8th May 1945 University, Guelma, Algeria

DOI:

https://doi.org/10.19139/soic-2310-5070-2807

Keywords:

Nonlinear Conjugate Gradient, Unconstrained Optimization, Strong Wolfe Line Search, Scilab.

Abstract

We introduce a novel hybrid conjugate gradient method for unconstrained optimization, combining the AlBayati-AlAssady and Wei-Yao-Liu approaches, where the convex parameter is determined using the conjugacy condition. Through rigorous theoretical analysis, we establish that the proposed method guarantees sufficient descent properties and achieves global convergence under the strong Wolfe conditions. Using the performance profile of Dolan and Moré, we confirm that our method, denoted as RN, consistently outperforms both classical (HS, FR, PRP and DY CG)  and hybrid (BAFR and BADY) methods, particularly for large-scale problems. 

Author Biography

  • Nabil Sellami, Laboratory of Analysis and Control of Differential Equations, Department of Mathematics, 8th May 1945 University, Guelma, Algeria
    Department of Mathematics, 8th May 1945 University, Guelma, Algeria

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Published

2025-10-15

Issue

Vol. 15 No. 1 (2026)

Section

Research Articles

Categories

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How to Cite

A Novel Hybrid Conjugate Gradient Algorithm for Solving Unconstrained Optimization Problems. (2025). Statistics, Optimization & Information Computing, 15(1), 380-395. https://doi.org/10.19139/soic-2310-5070-2807