2005, 1(1): 33-38. doi: 10.3934/jimo.2005.1.33

On the absence of duality gap for Lagrange-type functions

1. 

Engenharia de Sistemas e Computacao/COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

2. 

School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Australia

Received  July 2004 Revised  December 2004 Published  January 2005

Given a generic dual program we discuss the absence of duality gap for a family of Lagrange-type functions. We obtain necessary conditions that become sufficient ones under some additional assumptions. We also give examples of Lagrange-type functions for which this sufficient conditions hold.
Citation: Regina Sandra Burachik, Alex Rubinov. On the absence of duality gap for Lagrange-type functions. Journal of Industrial & Management Optimization, 2005, 1 (1) : 33-38. doi: 10.3934/jimo.2005.1.33
[1]

Chunrong Chen, T. C. Edwin Cheng, Shengji Li, Xiaoqi Yang. Nonlinear augmented Lagrangian for nonconvex multiobjective optimization. Journal of Industrial & Management Optimization, 2011, 7 (1) : 157-174. doi: 10.3934/jimo.2011.7.157

[2]

Jen-Yen Lin, Hui-Ju Chen, Ruey-Lin Sheu. Augmented Lagrange primal-dual approach for generalized fractional programming problems. Journal of Industrial & Management Optimization, 2013, 9 (4) : 723-741. doi: 10.3934/jimo.2013.9.723

[3]

Chunrong Chen. A unified nonlinear augmented Lagrangian approach for nonconvex vector optimization. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 495-508. doi: 10.3934/naco.2011.1.495

[4]

Qingsong Duan, Mengwei Xu, Yue Lu, Liwei Zhang. A smoothing augmented Lagrangian method for nonconvex, nonsmooth constrained programs and its applications to bilevel problems. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-21. doi: 10.3934/jimo.2018094

[5]

Mohamed Aly Tawhid. Nonsmooth generalized complementarity as unconstrained optimization. Journal of Industrial & Management Optimization, 2010, 6 (2) : 411-423. doi: 10.3934/jimo.2010.6.411

[6]

Qian Liu, Xinmin Yang, Heung Wing Joseph Lee. On saddle points of a class of augmented lagrangian functions. Journal of Industrial & Management Optimization, 2007, 3 (4) : 693-700. doi: 10.3934/jimo.2007.3.693

[7]

Caiping Liu, Heungwing Lee. Lagrange multiplier rules for approximate solutions in vector optimization. Journal of Industrial & Management Optimization, 2012, 8 (3) : 749-764. doi: 10.3934/jimo.2012.8.749

[8]

Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027

[9]

Dan Xue, Wenyu Sun, Hongjin He. A structured trust region method for nonconvex programming with separable structure. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 283-293. doi: 10.3934/naco.2013.3.283

[10]

Giancarlo Bigi. Componentwise versus global approaches to nonsmooth multiobjective optimization. Journal of Industrial & Management Optimization, 2005, 1 (1) : 21-32. doi: 10.3934/jimo.2005.1.21

[11]

Nobuko Sagara, Masao Fukushima. trust region method for nonsmooth convex optimization. Journal of Industrial & Management Optimization, 2005, 1 (2) : 171-180. doi: 10.3934/jimo.2005.1.171

[12]

Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-9. doi: 10.3934/jimo.2018136

[13]

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

[14]

Weijun Zhou, Youhua Zhou. On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization. Journal of Industrial & Management Optimization, 2013, 9 (4) : 893-899. doi: 10.3934/jimo.2013.9.893

[15]

Qilin Wang, S. J. Li. Higher-order sensitivity analysis in nonconvex vector optimization. Journal of Industrial & Management Optimization, 2010, 6 (2) : 381-392. doi: 10.3934/jimo.2010.6.381

[16]

Yuying Zhou, Gang Li. The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions. Numerical Algebra, Control & Optimization, 2014, 4 (1) : 9-23. doi: 10.3934/naco.2014.4.9

[17]

Fang Chen, Ning Gao, Yao- Lin Jiang. On product-type generalized block AOR method for augmented linear systems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 797-809. doi: 10.3934/naco.2012.2.797

[18]

Xiantao Xiao, Liwei Zhang, Jianzhong Zhang. On convergence of augmented Lagrangian method for inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2009, 5 (2) : 319-339. doi: 10.3934/jimo.2009.5.319

[19]

A. M. Bagirov, Moumita Ghosh, Dean Webb. A derivative-free method for linearly constrained nonsmooth optimization. Journal of Industrial & Management Optimization, 2006, 2 (3) : 319-338. doi: 10.3934/jimo.2006.2.319

[20]

Dan Li, Li-Ping Pang, Fang-Fang Guo, Zun-Quan Xia. An alternating linearization method with inexact data for bilevel nonsmooth convex optimization. Journal of Industrial & Management Optimization, 2014, 10 (3) : 859-869. doi: 10.3934/jimo.2014.10.859

2017 Impact Factor: 0.994

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (11)

Other articles
by authors

[Back to Top]