April  2008, 4(2): 385-391. doi: 10.3934/jimo.2008.4.385

Higher-order symmetric duality in multiobjective programming with invexity

1. 

Department of Mathematics, Chongqing Normal University, Chongqing 400047, China

2. 

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

3. 

Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, W.A. 6845, Australia

Received  November 2006 Revised  February 2008 Published  April 2008

In this paper, a pair of higher order symmetric dual models for multiobjective nonlinear programming is introduced. The weak, strong and converse duality theorems are proven for the formulated higher order symmetric dual programs under invexity conditions.
Citation: Xinmin Yang, Xiaoqi Yang, Kok Lay Teo. Higher-order symmetric duality in multiobjective programming with invexity. Journal of Industrial and Management Optimization, 2008, 4 (2) : 385-391. doi: 10.3934/jimo.2008.4.385
[1]

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

[2]

Liping Tang, Xinmin Yang, Ying Gao. Higher-order symmetric duality for multiobjective programming with cone constraints. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1873-1884. doi: 10.3934/jimo.2019033

[3]

Xinmin Yang. On second order symmetric duality in nondifferentiable multiobjective programming. Journal of Industrial and Management Optimization, 2009, 5 (4) : 697-703. doi: 10.3934/jimo.2009.5.697

[4]

Najeeb Abdulaleem. $ V $-$ E $-invexity in $ E $-differentiable multiobjective programming. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 427-443. doi: 10.3934/naco.2021014

[5]

Xinmin Yang, Xiaoqi Yang. A note on mixed type converse duality in multiobjective programming problems. Journal of Industrial and Management Optimization, 2010, 6 (3) : 497-500. doi: 10.3934/jimo.2010.6.497

[6]

Olga A. Brezhneva, Alexey A. Tret’yakov, Jerrold E. Marsden. Higher--order implicit function theorems and degenerate nonlinear boundary-value problems. Communications on Pure and Applied Analysis, 2008, 7 (2) : 293-315. doi: 10.3934/cpaa.2008.7.293

[7]

Najeeb Abdulaleem. Optimality and duality for $ E $-differentiable multiobjective programming problems involving $ E $-type Ⅰ functions. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022004

[8]

Daomin Cao, Guolin Qin. Liouville type theorems for fractional and higher-order fractional systems. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2269-2283. doi: 10.3934/dcds.2020361

[9]

R.S. Dahiya, A. Zafer. Oscillation theorems of higher order neutral type differential equations. Conference Publications, 1998, 1998 (Special) : 203-219. doi: 10.3934/proc.1998.1998.203

[10]

Qinghong Zhang, Gang Chen, Ting Zhang. Duality formulations in semidefinite programming. Journal of Industrial and Management Optimization, 2010, 6 (4) : 881-893. doi: 10.3934/jimo.2010.6.881

[11]

Gianni Di Pillo, Giampaolo Liuzzi, Stefano Lucidi. A primal-dual algorithm for nonlinear programming exploiting negative curvature directions. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 509-528. doi: 10.3934/naco.2011.1.509

[12]

Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial and Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115

[13]

Dariusz Bugajewski, Piotr Kasprzak. On mappings of higher order and their applications to nonlinear equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 627-647. doi: 10.3934/cpaa.2012.11.627

[14]

Feliz Minhós, Rui Carapinha. On higher order nonlinear impulsive boundary value problems. Conference Publications, 2015, 2015 (special) : 851-860. doi: 10.3934/proc.2015.0851

[15]

Mansoureh Alavi Hejazi, Soghra Nobakhtian. Optimality conditions for multiobjective fractional programming, via convexificators. Journal of Industrial and Management Optimization, 2020, 16 (2) : 623-631. doi: 10.3934/jimo.2018170

[16]

Xian-Jun Long, Nan-Jing Huang, Zhi-Bin Liu. Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs. Journal of Industrial and Management Optimization, 2008, 4 (2) : 287-298. doi: 10.3934/jimo.2008.4.287

[17]

Venkateswaran P. Krishnan, Vladimir A. Sharafutdinov. Ray transform on Sobolev spaces of symmetric tensor fields, I: Higher order Reshetnyak formulas. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2021076

[18]

Yanqun Liu. Duality in linear programming: From trichotomy to quadrichotomy. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1003-1011. doi: 10.3934/jimo.2011.7.1003

[19]

Tone-Yau Huang, Tamaki Tanaka. Optimality and duality for complex multi-objective programming. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 121-134. doi: 10.3934/naco.2021055

[20]

Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (105)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]