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A MODIFIED PROJECTED CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

Part of: Design of experiments Artificial intelligence (68Txx)

Published online by Cambridge University Press:  09 April 2013

SHUAI HUANG ,
ZHONG WAN  and
SONGHAI DENG
SHUAI HUANG
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, China email [email protected]@163.com
ZHONG WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, China email [email protected]@163.com
SONGHAI DENG
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, China email [email protected]@163.com
*
✉[email protected]
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Abstract

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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.

Keywords

PRP methodmodified conjugacy conditionprojected methodglobal convergence

MSC classification

Secondary: 90C30: Nonlinear programming 62K05: Optimal designs 68T37: Reasoning under uncertainty
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 3 , January 2013 , pp. 143 - 152
Copyright
Copyright ©2013 Australian Mathematical Society 

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