A New Preconditioned Inexact Line-Search Technique for Unconstrained Optimization

In this paper, we study the global convergence properties of the new class of preconditioned conjugate gradient descent algorithm, when applied to convex objective non-linear unconstrained optimization functions. We assume that a new inexact line search rule which is similar to the Armijo line-searc...

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Bibliographic Details
Published in:	AL-Rafidain journal of computer sciences and mathematics Vol. 9; no. 2; pp. 25 - 39
Main Authors:	Abbas Y. Al-Bayati, Ivan S. Latif
Format:	Journal Article
Language:	English
Published:	Mosul University 04.12.2012
Subjects:	inexact line-search preconditioned cg self-scaling vm-update unconstrained optimization
ISSN:	1815-4816, 2311-7990
Online Access:	Get full text
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Summary:	In this paper, we study the global convergence properties of the new class of preconditioned conjugate gradient descent algorithm, when applied to convex objective non-linear unconstrained optimization functions. We assume that a new inexact line search rule which is similar to the Armijo line-search rule is used. It's an estimation formula to choose a large step-size at each iteration and use the same formula to find the direction search. A new preconditioned conjugate gradient direction search is used to replace the conjugate gradient descent direction of ZIR-algorithm. Numerical results on twenty five well-know test functions with various dimensions show that the new inexact line-search and the new preconditioned conjugate gradient search directions are efficient for solving unconstrained nonlinear optimization problem in many situations.
ISSN:	1815-4816 2311-7990
DOI:	10.33899/csmj.2012.163698