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

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).

(1959).

[2] Sulaiman, N.A. and Abulrahim, B. K., "Arithmetic average transformation technique to solve

multi-objective quadratic programming", Vol.15, No.1, (2013).

[3] Sen., Ch.,"A new approach for multi-objective rural development planning", The India Economic

Journal, Vol. 30, No. 4, pp.91-96, (1983).

[4] Sulaiman, N., A., and Abdul-Rahim, B., K., "Optimal cutting plane procedure for MOQPP", Jornal

of koya University, ISSN.2073-20713, No-20, pp.119-130, (2011).

[5] Sulaiman, N. A. and Sadiq, G. W., "studied solving the multi-objective linear programming

problem using mean and median value", Al-Rafiden Journal of computer sciences and mathematics,

mosul university, Vol.3, No.1, pp. 69-83(2006).

[6] Al-Barzinji, S. H. A., "Extreme Point Optimization Technique in Mathematical Programming",

M.Sc. Thesis, University of Salahaddin, Erbil/ Iraq(1988).

[7] Sulaiman, N., A., and Abdul-Rahim, B., K., "studied New arithmetic average technique to solve

Multi-objective linear fractional programming problem and its comparison with other

techniques",IJRRAS, Vol.18, No.2, (2014).

[8] Sulaiman, N., A., and Nawkhass, M. A., "using short-hierarchical method to solve MOLFPP", 2nd

scientific conference of Garmian University, may/6,7(2015).

[9] Abdul Rahim, B. K., "Solving quadratic programming with extreme point", MSc. Thesis, Sulaimani

University, Sulaimani-Iraq (2011).

[11]http://en.wikipedia.org/wiki/Geometric_mean

[12] http://www.columbia.edu/~cs2035/courses/ieor4600.S07/lec1.pdf

[13] Sulaiman, N. A., "Extreme Point Quadratic Programming Problem Techniques", M.Sc.,Thesis,

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).

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).

[2] Sulaiman, N.A. and Abulrahim, B. K., "Arithmetic average transformation technique to solve

multi-objective quadratic programming", Vol.15, No.1, (2013).

[3] Sen., Ch.,"A new approach for multi-objective rural development planning", The India Economic

Journal, Vol. 30, No. 4, pp.91-96, (1983).

[4] Sulaiman, N., A., and Abdul-Rahim, B., K., "Optimal cutting plane procedure for MOQPP", Jornal

of koya University, ISSN.2073-20713, No-20, pp.119-130, (2011).

[5] Sulaiman, N. A. and Sadiq, G. W., "studied solving the multi-objective linear programming

problem using mean and median value", Al-Rafiden Journal of computer sciences and mathematics,

mosul university, Vol.3, No.1, pp. 69-83(2006).

[6] Al-Barzinji, S. H. A., "Extreme Point Optimization Technique in Mathematical Programming",

M.Sc. Thesis, University of Salahaddin, Erbil/ Iraq(1988).

[7] Sulaiman, N., A., and Abdul-Rahim, B., K., "studied New arithmetic average technique to solve

Multi-objective linear fractional programming problem and its comparison with other

techniques",IJRRAS, Vol.18, No.2, (2014).

[8] Sulaiman, N., A., and Nawkhass, M. A., "using short-hierarchical method to solve MOLFPP", 2nd

scientific conference of Garmian University, may/6,7(2015).

[9] Abdul Rahim, B. K., "Solving quadratic programming with extreme point", MSc. Thesis, Sulaimani

University, Sulaimani-Iraq (2011).

[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

[13] Sulaiman, N. A., "Extreme Point Quadratic Programming Problem Techniques", M.Sc.,Thesis,

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).