Solving Quadratic Fractional Programming Problem
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Abstract
In this paper the fractional Quadratic objective programming problem (QFPP) with linear constraints, has been defined and developed. The special case for this problem was solved by using the Wolfe’s method and a modified simplex approach, by suggesting an algorithm for each method to solve the problem. The computer application for algorithms was tested on a number of numerical examples, consequently reliable results have been found.References
[1] A. Antoniou, Wu-Sheng Lu, Practical Optimization: Algorithms and Engineering Applications, Department of Electrical and Computer Engineering University of Victoria, Canada. (2007). 675.
[2] A. Beck, A. Ben-Tal and M. Teboulle Finding A Global Optimal Solution For A Quadratically Constrained Fractional Quadratic Problem With Applications To The Regularized Total Least Squares, Society for Industrial and Applied Mathematics Siam J. Matrix Anal. Appl.Vol. 28, No. 2, (2006), 425–445.
[3] M, Hasan. (July), A Technique for Solving Special Type Quadratic Programming Problems, Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh, Dhaka Univ. J. Sci. 60(2): (2012), 209-215.
[4] M. Borza, A. Rambely, M. Saraj, Solving Linear Fractional Programming Problems with Interval Coefficients in the Objective Function. A New Approach, Department of Mathematics, Faculty of Mathematical Sciences & Computer, Shahid Chamran University, Ahvaz-Iran, Applied Mathematical Sciences, Vol. 6, 2012, no. 69, (2012), 3443 – 3452.
[5] M. Biggs, Nonlinear Optimization with Financial Applications, Kluwer Academic Publishers, England. (2005),41.
View more references (7)
[6] M. Fukushima, Sh. Hayashi, , Quadratic Fractional Programming Problems with Quadratic Constraints, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University. (2008).
[7] M.Vankova, Algorithms for the Solution of the Quadratic Programming Problem, the Faculty of Science at the University Of Port Elizabeth. (2004), 36.
[8] P. Amaral, I. Bomze, J. Judice, Copositivity and Constrained Fractional Quadratic Problems, www.optimization online.org/ DB_FILE /2010 /06/2641.pdf, (2011).
[9] P. Wolfe, the Simplex Method for Quadratic Programming Economics, Vol.27,1959, 382-398.
[10] R. Singh, Optimization Methods and Quadratic Programming, Department of Mathematics National Institute of Technology, Rourkela Odisha, India, (2012), 28.
[11] S. Sharma, Operation Research, Kedar Nath Ram Nath BCO. Meerut, India. (1988).
[12] S, Sharma, Nonlinear and Dynamic Programming, Kedar Nath Ram Nath and CO, Meerut. (1980).