Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints

Affiliation(s)

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India.

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India.

ABSTRACT

In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function in the presence of equality and inequality constraints. As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-Weir type dual to this problem is formulated and various duality results are established under generalized invexity assumptions. Finally, a special case is deduced from our result.

Cite this paper

Husain, I. and Jain, V. (2013) Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints.*Open Journal of Modelling and Simulation*, **1**, 7-13. doi: 10.4236/ojmsi.2013.12002.

Husain, I. and Jain, V. (2013) Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints.

References

[1] B. Mond, “A Class of Nondifferentiable Mathematical Programming Problems,” Journal of Mathematical Analysis and Applications, Vol. 46, No. 1, 1974, pp. 169-174. doi:10.1016/0022-247X(74)90289-3

[2] S. Chandra, B. D. Craven and B. Mond, “Generalized Concavity and Duality with a Square Root Term,” Optimization, Vol. 16, No. 5, 1985, pp. 654-662. doi:10.1080/02331938508843062

[3] J. Zhang and B. Mond, “Duality for a Nondifferentiable Programming Problem,” Bulletin of the Australian Mathematical Society, Vol. 55, No. 1, 1997, pp. 29-44. doi:10.1017/S0004972700030513

[4] S. N. Lal, B. Nath and A. Kumar, “Duality for Some Nondifferentiable Static Multiobjective Programming Problems,” Journal of Mathematical Analysis and Applications, Vol. 186, No. 3, 1994, pp. 862-867. doi:10.1006/jmaa.1994.1337

[5] S. J. Kim, M. H. Kim and D. S. Kim, “Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems,” Journal of Optimization Theory and Applications, Vol. 129, No. 1, 2006, pp. 131-146. doi:10.1007/s10957-006-9048-1

[6] X. M. Yang, K. L. Teo and X. Q. Yang, “Duality for a Class of Nondifferentiable Multiobjective Programming Problem,” Journal of Mathematical Analysis and Applications, Vol. 252, No. 2, 2000, pp. 999-1005. doi:10.1006/jmaa.2000.6991

[7] F. Riesz and B. Sz.-Nagy, “Functional Analysis,” Fredrick Ungar Publishing Co., New York, 1955.

[8] I. Husain and S. K. Srivastav, “On Nondifferentiable Non- linear Programming,” Journal of Applied Mathematics and Bioinformatics, Vol. 3, No. 2, 2013, pp. 45-64.

[9] V. Chankong and Y. Y. Haimes, “Multiobjective Decision Making Theory and Methodology,” North-Holland, New York, 1983.

[1] B. Mond, “A Class of Nondifferentiable Mathematical Programming Problems,” Journal of Mathematical Analysis and Applications, Vol. 46, No. 1, 1974, pp. 169-174. doi:10.1016/0022-247X(74)90289-3

[2] S. Chandra, B. D. Craven and B. Mond, “Generalized Concavity and Duality with a Square Root Term,” Optimization, Vol. 16, No. 5, 1985, pp. 654-662. doi:10.1080/02331938508843062

[3] J. Zhang and B. Mond, “Duality for a Nondifferentiable Programming Problem,” Bulletin of the Australian Mathematical Society, Vol. 55, No. 1, 1997, pp. 29-44. doi:10.1017/S0004972700030513

[4] S. N. Lal, B. Nath and A. Kumar, “Duality for Some Nondifferentiable Static Multiobjective Programming Problems,” Journal of Mathematical Analysis and Applications, Vol. 186, No. 3, 1994, pp. 862-867. doi:10.1006/jmaa.1994.1337

[5] S. J. Kim, M. H. Kim and D. S. Kim, “Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems,” Journal of Optimization Theory and Applications, Vol. 129, No. 1, 2006, pp. 131-146. doi:10.1007/s10957-006-9048-1

[6] X. M. Yang, K. L. Teo and X. Q. Yang, “Duality for a Class of Nondifferentiable Multiobjective Programming Problem,” Journal of Mathematical Analysis and Applications, Vol. 252, No. 2, 2000, pp. 999-1005. doi:10.1006/jmaa.2000.6991

[7] F. Riesz and B. Sz.-Nagy, “Functional Analysis,” Fredrick Ungar Publishing Co., New York, 1955.

[8] I. Husain and S. K. Srivastav, “On Nondifferentiable Non- linear Programming,” Journal of Applied Mathematics and Bioinformatics, Vol. 3, No. 2, 2013, pp. 45-64.

[9] V. Chankong and Y. Y. Haimes, “Multiobjective Decision Making Theory and Methodology,” North-Holland, New York, 1983.