2017•Journal of Physics Conference SeriesOpen access

Hybrid DFP-CG method for solving unconstrained optimization problems

Wan Farah Hanan Wan Osman, Mohd Asrul Hery Ibrahim, Mustafa Mamat

Abstract

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

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Key concepts: Broyden–Fletcher–Goldfarb–Shanno algorithm, Conjugate gradient method, Hessian matrix, Nonlinear conjugate gradient method, Descent (aeronautics), Convergence (economics), Quasi-Newton method, Gradient method