A modified projected conjugate gradient algorithm for unconstrained optimization problems

Shuai Huang, Songhai Deng, Zhong Wan

Abstract


We propose a modified projected Polak–Ribière–Polyak (PRP) conjugate gradient method, where a modified conjugacy condition and a method which generates sufficient descent directions are incorporated into the construction of a suitable conjugacy parameter. It is shown that the proposed method is a modification of the PRP method and generates sufficient descent directions at each iteration. With an Armijo- type line search, the theory of global convergence is established under two weak assumptions. Numerical experiments are employed to test the efficiency of the algorithm in solving some benchmark test problems available in the literature. The numerical results obtained indicate that the algorithm outperforms an existing similar algorithm in requiring fewer function evaluations and fewer iterations to find optimal solutions with the same tolerance.

doi:10.1017/S1446181113000084

Keywords


PRP method, modified conjugacy condition, projected method, global convergence



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5910



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.