# American Institute of Mathematical Sciences

July  2013, 9(3): 525-530. doi: 10.3934/jimo.2013.9.525

## 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, China 3 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received  May 2012 Revised  March 2013 Published  April 2013

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].
Citation: Xinmin Yang, Jin Yang, Heung Wing Joseph Lee. Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs. Journal of Industrial and Management Optimization, 2013, 9 (3) : 525-530. doi: 10.3934/jimo.2013.9.525
##### 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.

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##### 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.
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