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A Proposed Method to Solve Quadratic Fractional Programming Problem by Converting to Double Linear Programming

Amir Sabir Majeed1 , Fadhil Salman Abed2

1 Department of Mechanic, College of Technical Engineering,Sulaimani Polytechnic University, 
Kurdistan Region, Iraq

2 Department of Mechanic, College of Technical Engineering, Sulaimani Polytechnic University, Kalar Technical Institute, Kurdistan Region, Iraq

Original : 7 Spet. 2015, Revised: 23 May 2016, Accepted: 5 June 2016, Published online: 20 March 2017



Quadratic fractional program is an optimization problem which solving the problem by minimizes or maximizes a quadratic fractional objective function subject to finite number of linear inequality (equality constraints) . In our paper, we proposed a new method to solve quadratic fractional programming problem (QFPP),the objective function of quadratic optimization has linear factorized as product of two linear functions, the two positive linear functions solved separately by using simplex method. These are useful in solving the problem in multi-application, like economics, hospital and health, engineering problem, financial planning etc.
In our paper, it was addressed to a variety of examples and the results were encouraging and accurate comparison with other methods with ease in the solution.

Key Words:
QFPP, LP, simplex method, Optimality Conditions, quadratic programming, fractional programming, linearization.


[1] B. Abdulrahim, "Solving Quadratic Programming Problem with ExtremePoints", M.Sc. Thesis, University of Sulaimani, Sulaimani/Iraq. (2011).

[2] Bazaraa, S.H.D. Sherali and C.M. Shetty ,"Nonlinear Programming: Theory and Algorithms",(2nd ed.), John Wiley & Sons Inc., New York, (1993).

[3] Dinkelbach, W.,"On Nonlinear Fractional Programming", Management Science, Vol. 13, pp. 492-498, (1967).

[4] Archana kuruna and. S. R. arora, "An Algorithm for Solving Quadratic Fractional Program with Linear Homogeneous Constraints", Vietnam Journal of Mathematics Vol. 39. No. 4. pp. 391-404. (2011).

[5] M.Bigges,"Nonlinear Optimization with Finantial Applications", Kluwer Academic Publishers, England. (2005).

[6] Jeffrey Wheeler , "Mathematical Models for Consultants, Linear Programming", Carngie Mellon University, Math 70-460. (2009).

[7] Robert Robere, "Interior Point Methods and Linear Programming", University of Toronto December 13, (2012).

[8] Nicolas W. Sawaya, Ignacio E. Grossmann, "A cutting plane method for solving linear generalized disjunctive programming problems", Computers and Chemical Engineering Vol. 29, pp. 1891–1913. (2005).

[9] Bitran, G ,R. and Novaes, A.G., "Linear programming with a Fractional Objective Function", University of Soa Paulo. Brazil. (1972).