Descent Condition for a Scalar Parameter of Spectral HS (SpHS) Conjugate Gradient Method
U A Yakubu1, M Mamat2, A V Mandara3, A Iguda4, S Murtala5, M A Mohamed6
1Usman Abbas Yakubu, Mathematics, Northwest University, Kano, Nigeria.
2Mustafa Mamat Faculty of Informatics and Computing, University Sultan Zainal Abidin, Kuala Terengganu, Malaysia.
3Abba Vulgue Mandara, Department of Mathematic, University of Maiduguri, Borno, Nigeria.
4Abdul Iguda, Mathematical Sciences, Bayero University, Kano, Nigeria.
5Salisu Murtala, Department of Mathematics, Federal University Dutse, Jigawa, Nigeria.
6Mohamad Afendee Mohamed, Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Terengganu, Malaysia.

Manuscript received on November 11, 2019. | Revised Manuscript received on November 20 2019. | Manuscript published on 30 November, 2019. | PP: 11464-11467 | Volume-8 Issue-4, November 2019. | Retrieval Number: B3003078219/2019©BEIESP | DOI: 10.35940/ijrte.B3003.118419

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Abstract: Spectral conjugate gradient method has been used in most cases as an alternative to the conjugate gradient (CG) method in order to solve nonlinear unconstrained problems. In this paper, we introduced a spectral parameter of HS conjugate gradient method resultant from the classical CG search direction and used some of the standard test functions with numerous variables to prove its sufficient descent and global convergence properties, the numerical outcome is verified by exact line search procedures.
Keywords: Unconstrained Optimization, Sufficient Descent Property, Spectral Conjugate Gradient, Global Convergence.
Scope of the Article: Cross-Layer Optimization.