April  2008, 4(2): 287-298. doi: 10.3934/jimo.2008.4.287

Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs

1. 

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China, China

2. 

Department of Applied Mathematics, Southwest Petroleum University, Chengdu, Sichuan 610500, China

Received  January 2007 Revised  August 2007 Published  April 2008

In this paper, a class of nondifferentiable multiobjective fractional programs is studied, in which every component of the objective function contains a term involving the support function of a compact convex set. Kuhn-Tucker necessary and sufficient optimality conditions, duality and saddle point results for weakly efficient solutions of the nondifferentiable multiobjective fractional programming problems are given. The results presented in this paper improve and extend some the corresponding results in the literature.
Citation: 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
[1]

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

[2]

Aleksandar Jović. Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022025

[3]

Yuhua Sun, Laisheng Wang. Optimality conditions and duality in nondifferentiable interval-valued programming. Journal of Industrial and Management Optimization, 2013, 9 (1) : 131-142. doi: 10.3934/jimo.2013.9.131

[4]

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

[5]

Xian-Jun Long, Jing Quan. Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 361-370. doi: 10.3934/naco.2011.1.361

[6]

Xiao-Bing Li, Qi-Lin Wang, Zhi Lin. Optimality conditions and duality for minimax fractional programming problems with data uncertainty. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1133-1151. doi: 10.3934/jimo.2018089

[7]

Ram U. Verma. General parametric sufficient optimality conditions for multiple objective fractional subset programming relating to generalized $(\rho,\eta,A)$ -invexity. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 333-339. doi: 10.3934/naco.2011.1.333

[8]

Xiuhong Chen, Zhihua Li. On optimality conditions and duality for non-differentiable interval-valued programming problems with the generalized (F, ρ)-convexity. Journal of Industrial and Management Optimization, 2018, 14 (3) : 895-912. doi: 10.3934/jimo.2017081

[9]

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

[10]

Nazih Abderrazzak Gadhi, Fatima Zahra Rahou. Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021216

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

Yasmine Cherfaoui, Mustapha Moulaï. Biobjective optimization over the efficient set of multiobjective integer programming problem. Journal of Industrial and Management Optimization, 2021, 17 (1) : 117-131. doi: 10.3934/jimo.2019102

[17]

Matthew H. Henry, Yacov Y. Haimes. Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty. Journal of Industrial and Management Optimization, 2009, 5 (4) : 791-824. doi: 10.3934/jimo.2009.5.791

[18]

Tim Hoheisel, Maxime Laborde, Adam Oberman. A regularization interpretation of the proximal point method for weakly convex functions. Journal of Dynamics and Games, 2020, 7 (1) : 79-96. doi: 10.3934/jdg.2020005

[19]

Yibing Lv, Tiesong Hu, Jianlin Jiang. Penalty method-based equilibrium point approach for solving the linear bilevel multiobjective programming problem. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1743-1755. doi: 10.3934/dcdss.2020102

[20]

Xiayang Zhang, Yuqian Kong, Shanshan Liu, Yuan Shen. A relaxed parameter condition for the primal-dual hybrid gradient method for saddle-point problem. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022008

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (308)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]