Title: Solution method of optimisation problem based on a modified Armijo-type line search

Authors: Zhong Wan; Yu Chen; XiaoDong Zheng

Addresses: School of Mathematics and Statistics, Central South University, Changsha, 410083, China ' School of Mathematics and Statistics, Central South University, Changsha, 410083, China ' School of Mathematics and Statistics, Central South University, Changsha, 410083, China

Abstract: In this paper, a new inexact line search rule is presented for solving a class of fundamental unconstrained optimisation problems. As a modified version of the standard Armijo line search rule, it incorporates the information of the second order derivative of objective function into determining a suitable step length based on the more accurate approximation of objective function. Owing to this line search, a greater reduction of objective function may be obtained at each iteration as well as with less cost of computation. Combined with a choice of descent search direction, a well defined algorithm is developed, where the line search rule allows the initial step length to be adjusted automatically such that the numerical performance of algorithm is improved. Under some mild assumptions, global convergence is established for the algorithm. Numerical results demonstrate that the proposed method is promising, especially in comparison with the existing methods.

Keywords: unconstrained optimisation; inexact line search rule; global convergence; Armijo-type line search.

DOI: 10.1504/IJCSE.2015.072643

International Journal of Computational Science and Engineering, 2015 Vol.11 No.3, pp.322 - 329

Available online: 23 Oct 2015 *

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