An Efficient Fifth-Order Method for Linear Optimization

Youssef EL Foutayeni (), Hicham EL Bouanani () and Mohamed Khaladi ()
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Youssef EL Foutayeni: Hassan II University, Faculté des Sciences Ben M’Sik, Av Driss El Harti
Hicham EL Bouanani: Hassan II University
Mohamed Khaladi: Cadi Ayyad University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 12, 189-204

Abstract: Abstract In this paper, we present an efficient fifth-order method for solving the standard linear optimization problems. In order to do this, we show that solving this problem is equivalent to solving a system of nonlinear equations. Therefore, we build a sequence of functions giving an approximate solution of this system. To find this approximation, we give an algorithm, which is based on the idea of the Sharma’s method. Computational efficiency, in its general form, is discussed, and a comparison between the efficiency of proposed technique and existing one is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples.

Keywords: Linear optimization; Primal-dual problem; Fifth-order method; System of nonlinear equations; 90C05; 90C51; 90C20; 90C60 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0896-z

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