A New Hybrid Conjugate Gradient Method Based on Secant Equation for Solving Large Scale Unconstrained Optimization Problems

Iranian Journal of Optimization

مقاله 4، دوره 12، شماره 1، شهریور 2020، صفحه 33-44   

نوع مقاله: Research Paper

نویسندگان

Nasiru Salihu^{* 1}؛ Mathew Remilekun Odekunle²؛ Mohammed Yusuf Waziri³؛ Abubakar Sani Halilu⁴

¹Department of Mathematics, School of Physical Science, Moddibo Adama University of Technology, Yola.

²Department of Mathematics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria.

³Department of Mathematical Sciences, Faculty of Sciences, Bayero University, Kano, Nigeria.

⁴Department of Mathematics and Computer Science, Sule Lamido University, Ka n Hausa, Nigeria.

چکیده

There exist large varieties of conjugate gradient algorithms. In order to take advantage of the attractive features of Liu and Storey (LS) and Conjugate Descent (CD) conjugate gradient methods, we suggest hybridization of these methods in which the parameter  is computed as a convex combination of  and respectively which the conjugate gradient (update) parameter was obtained from Secant equation. The algorithm generates descent direction and when the iterate jam, the direction satisfy sufficient descent condition. We report numerical results demonstrating the efficiency of our method. The hybrid computational scheme outperform or comparable with known conjugate gradient algorithms. We also show that our method converge globally using strong Wolfe condition.

کلیدواژه‌ها

Unconstrained optimization؛ conjugate gradient algorithm؛ large scale optimization problem؛ secant equation؛ global convergence