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

show all references

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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