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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 965104, 8 pages
http://dx.doi.org/10.1155/2014/965104
Research Article

Accelerated Double Direction Method for Solving Unconstrained Optimization Problems

1Faculty of Science, University of Priština, Lole Ribara 29, 28000 Kosovska Mitrovica, Serbia
2Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia

Received 9 December 2013; Revised 2 March 2014; Accepted 4 March 2014; Published 2 April 2014

Academic Editor: J. J. Judice

Copyright © 2014 Milena J. Petrović and Predrag S. Stanimirović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An iterative method for solving a minimization problem of unconstrained optimization is presented. This multistep curve search method uses the specific form of iteration with two direction parameters, the approximation of Hessian by appropriately constructed diagonal matrix, and the inexact line search procedure. It is proved that constructed numerical process is well defined under some assumptions. Considering certain conditions, the method is linearly convergent for uniformly convex and strictly convex quadratic functions. Numerical results arising from defined algorithms are also presented and analyzed.