Research Article Open Access

New Scaled Sufficient Descent Conjugate Gradient Algorithm for Solving Unconstraint Optimization Problems

Abbas Y. AL-Bayati1 and Rafiq S. Muhammad2
  • 1 , Afganistan
  • 2 ,
Journal of Computer Science
Volume 6 No. 5, 2010, 511-518

DOI: https://doi.org/10.3844/jcssp.2010.511.518

Submitted On: 22 April 2010 Published On: 31 May 2010

How to Cite: AL-Bayati, A. Y. & Muhammad, R. S. (2010). New Scaled Sufficient Descent Conjugate Gradient Algorithm for Solving Unconstraint Optimization Problems. Journal of Computer Science, 6(5), 511-518. https://doi.org/10.3844/jcssp.2010.511.518

Abstract

Problem statement: The scaled hybrid Conjugate Gradient (CG) algorithm which usually used for solving non-linear functions was presented and was compared with two standard well-Known NAG routines, yielding a new fast comparable algorithm. Approach: We proposed, a new hybrid technique based on the combination of two well-known scaled (CG) formulas for the quadratic model in unconstrained optimization using exact line searches. A global convergence result for the new technique was proved, when the Wolfe line search conditions were used. Results: Computational results, for a set consisting of 1915 combinations of (unconstrained optimization test problems/dimensions) were implemented in this research making a comparison between the new proposed algorithm and the other two similar algorithms in this field. Conclusion: Our numerical results showed that this new scaled hybrid CG-algorithm substantially outperforms Andrei-sufficient descent condition (CGSD) algorithm and the well-known Andrei standard sufficient descent condition from (ACGA) algorithm.

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Keywords

  • Unconstrained optimization
  • hybrid conjugate gradient
  • scaled conjugate gradient
  • sufficient descent condition
  • conjugacy condition