Malaysian Journal of Mathematical Sciences, March 2024, Vol. 18, No. 1

A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

Ishak M. A. I. and Marjugi S. M.

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Received date: 19 September 2023
Accepted date: 3 January 2024

The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solving unconstrained optimization problems. This algorithm utilizes a search direction that combines Liu-Storey (LS) and Conjugate Descent (CD) CG coefficients and standardizes it using a spectral which acts as a scheme for the choices of the conjugate parameters. This resultant direction closely approximates the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton direction, known for its bounded nature and compliance with the sufficient descent condition. The paper establishes the global convergence under standard Wolfe conditions and some appropriate assumptions. Additionally, the numerical experiments were conducted to emphasize the robustness and superior efficiency of this hybrid algorithm in comparison to existing approaches.

Keywords: unconstrained optimization; three-termconjugate gradient; memoryless quasi-Newton method; line search; global convergence



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