Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs

Xinmin Yang; Jin Yang; Heung Wing Joseph Lee

doi:10.3934/jimo.2013.9.525

Article Contents

2013, Volume 9, Issue 3: 525-530. Doi: 10.3934/jimo.2013.9.525

This issue Previous Article Control parametrization and finite element method for controlling multi-species reactive transport in a circular pool Next Article A conic approximation method for the 0-1 quadratic knapsack problem

Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs

1.
Department of Mathematics, Chongqing Normal University, Chongqing 400047
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
3.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: April 30, 2012

Revised: February 28, 2013

Published: June 2013

Abstract Related Papers Cited by

Abstract

In this paper, we establish a strong duality theorem for Mond-Weir type multiobjective higher order nondifferentiable symmetric dual programs. Our works correct some deficiencies in recent papers [higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290(2004)423-435] and [A note on higher-order nondifferentiable symmetric duality in multiobjective programming, Appl. Math. Letters 24(2011) 1308-1311].

Keywords:

Multiobjective programming,
higher order Mond-Weir symmetric dual model,
strong duality theorem,
nondifferentiablity.

Mathematics Subject Classification: Primary: 90C29, 49J52, 90C46.

Citation:

Related Papers

Cited by

References

[1]	R. P. Agarwal, I. Ahmad and S. K. Gupta, A note on higher order nondifferentiable symmetric duality in multiobjective programming, Applied Mathematics Letters, 24 (2011), 1308-1311.doi: 10.1016/j.aml.2011.02.021.
[2]	A. Batatorescu, V. Preda and M Beldiman, Higher-order symmetric multiobjective duality involving generalized $(F,\rho,\gamma,b)$-convexity, Rev. Roumaine Math. Pures Appl., 52 (2007), 619-630.
[3]	X. Chen, Higher order symmetric duality in non-differentiable multiobjective programming problems, J. Math. Anal. Appl., 290 (2004), 423-435.doi: 10.1016/j.jmaa.2003.10.004.
[4]	M. Schechter, More on subgradient duality, J. Math. Anal. Appl., 71 (1979), 251-262.doi: 10.1016/0022-247X(79)90228-2.
[5]	X. M. Yang, On second order symmetric duality in nondifferentiable multiobjective programming, Journal of Industrial and Management Optimization, 5 (2009), 697-703.doi: 10.3934/jimo.2009.5.697.
[6]	X. M. Yang, On symmetric and self duality in vector optimization problem, Journal of Industrial and Management Optimization, 7 (2011), 523-529.doi: 10.3934/jimo.2011.7.523.
[7]	X. M. Yang and X. Q. Yang, A note on mixed type converse duality in multiobjective programming problems, Journal of Industrial and Management Optimization, 6 (2010), 497-500.doi: 10.3934/jimo.2010.6.497.
[8]	X. M. Yang, X. Q. Yang and K. L. Teo, Higher-order symmetric duality in multiobjective programming with invexity, Journal of Industrial and Management Optimization, 4 (2008), 385-391.doi: 10.3934/jimo.2008.4.385.
[9]	X. M. Yang, X. Q. Yang, K. L. Teo and S. H. Hou, Second-order symmetric duality in non-differentiable multiobjective programming with $F$-convexity, European J. Oper. Res., 164 (2005), 406-416.doi: 10.1016/j.ejor.2003.04.007.