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Nejmaddin A. Sulaiman1, Ronak M. Abdullah2 and Snur O. Abdull2
1 Mathematical Department, College of Education/ Salahaddin University -Erbil.
2 Mathematics Department, School of Science /University of Sulaimani.
DOI: https://doi.org/10.17656/jzs.10535
Abstract
In this paper, we suggested a new technique by using optimal geometric average for the value of functions, to solve extreme point multi- objective quadratic programming problem (EPMOQPP), via transforming it to extreme point single-objective quadratic programming problem(EPSOQPP), then solve the problem by Wolfe’s method [1] , and an algorithm is given for its solution, also using cutting plane technique when the optimal value of the objective function is not an extreme point of constraints, the computer application for this algorithm was tested on a number of numerical examples, which are also solved by several techniques (Chandra Sen.'s, mean, median, and optimal arithmetic). After comparing, the results indicate that the new technique is best than others as shown in table (3).
Key Words: Optimal geometric average, EPMOQPP, Cutting plane technique
References:
[1] Wolfe, P.,"The simplex method for quadratic programming", Econometrical, Vol.27, pp. 382-389,
(1959).
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multi-objective quadratic programming", Vol.15, No.1, (2013).
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[10] http://en.wikipedia.org/wiki/Quadratic_programming#cite_note-1
[11]http://en.wikipedia.org/wiki/Geometric_mean
[12] http://www.columbia.edu/~cs2035/courses/ieor4600.S07/lec1.pdf
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University of Salahaddin, Hawler\Iraq (1989).
[14] Kirby M. J., love H. R. and Swarup K., "Extreme point programming with non-linear
constraints", discrete mathematics, Vol. 15, pp. 345-365 (1973).
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