# 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 & 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. doi: 10.1016/j.aml.2011.02.021. Google Scholar [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. Google Scholar [3] X. Chen, Higher order symmetric duality in non-differentiable multiobjective programming problems,, J. Math. Anal. Appl., 290 (2004), 423. doi: 10.1016/j.jmaa.2003.10.004. Google Scholar [4] M. Schechter, More on subgradient duality,, J. Math. Anal. Appl., 71 (1979), 251. doi: 10.1016/0022-247X(79)90228-2. Google Scholar [5] X. M. Yang, On second order symmetric duality in nondifferentiable multiobjective programming,, Journal of Industrial and Management Optimization, 5 (2009), 697. doi: 10.3934/jimo.2009.5.697. Google Scholar [6] X. M. Yang, On symmetric and self duality in vector optimization problem,, Journal of Industrial and Management Optimization, 7 (2011), 523. doi: 10.3934/jimo.2011.7.523. Google Scholar [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. doi: 10.3934/jimo.2010.6.497. Google Scholar [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. doi: 10.3934/jimo.2008.4.385. Google Scholar [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. doi: 10.1016/j.ejor.2003.04.007. Google Scholar

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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. doi: 10.1016/j.aml.2011.02.021. Google Scholar [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. Google Scholar [3] X. Chen, Higher order symmetric duality in non-differentiable multiobjective programming problems,, J. Math. Anal. Appl., 290 (2004), 423. doi: 10.1016/j.jmaa.2003.10.004. Google Scholar [4] M. Schechter, More on subgradient duality,, J. Math. Anal. Appl., 71 (1979), 251. doi: 10.1016/0022-247X(79)90228-2. Google Scholar [5] X. M. Yang, On second order symmetric duality in nondifferentiable multiobjective programming,, Journal of Industrial and Management Optimization, 5 (2009), 697. doi: 10.3934/jimo.2009.5.697. Google Scholar [6] X. M. Yang, On symmetric and self duality in vector optimization problem,, Journal of Industrial and Management Optimization, 7 (2011), 523. doi: 10.3934/jimo.2011.7.523. Google Scholar [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. doi: 10.3934/jimo.2010.6.497. Google Scholar [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. doi: 10.3934/jimo.2008.4.385. Google Scholar [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. doi: 10.1016/j.ejor.2003.04.007. Google Scholar
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