Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications
Author
Abstract
Suggested Citation
DOI: 10.1007/s10957-008-9455-6
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- X. X. Huang & X. Q. Yang, 2003. "A Unified Augmented Lagrangian Approach to Duality and Exact Penalization," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 533-552, August.
- Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
- A. M. Rubinov & X. X. Huang & X. Q. Yang, 2002. "The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 775-791, November.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Regina S. Burachik & Alfredo N. Iusem & Jefferson G. Melo, 2013. "An Inexact Modified Subgradient Algorithm for Primal-Dual Problems via Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 108-131, April.
- R. S. Burachik & A. N. Iusem & J. G. Melo, 2010. "Duality and Exact Penalization for General Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 125-140, October.
- Yu Zhou & Jin Zhou & Xiao Yang, 2014. "Existence of augmented Lagrange multipliers for cone constrained optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 243-260, February.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- J. Zhai & X. X. Huang, 2014. "Calmness and Exact Penalization in Vector Optimization under Nonlinear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 856-872, September.
- S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part I: Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 738-762, June.
- S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 763-782, June.
- Qian Liu & Wan Tang & Xin Yang, 2009. "Properties of saddle points for generalized augmented Lagrangian," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 111-124, March.
- X. Q. Yang & Z. Q. Meng, 2007. "Lagrange Multipliers and Calmness Conditions of Order p," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 95-101, February.
- Angelia Nedić & Asuman Ozdaglar, 2008. "Separation of Nonconvex Sets with General Augmenting Functions," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 587-605, August.
- C. Y. Wang & X. Q. Yang & X. M. Yang, 2007. "Unified Nonlinear Lagrangian Approach to Duality and Optimal Paths," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 85-100, October.
- Jinchuan Zhou & Jein-Shan Chen, 2015. "On the existence of saddle points for nonlinear second-order cone programming problems," Journal of Global Optimization, Springer, vol. 62(3), pages 459-480, July.
- C. Lalitha, 2010. "A new augmented Lagrangian approach to duality and exact penalization," Journal of Global Optimization, Springer, vol. 46(2), pages 233-245, February.
- Chao Kan & Wen Song, 2015. "Augmented Lagrangian Duality for Composite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 763-784, June.
- Yu Zhou & Jin Zhou & Xiao Yang, 2014. "Existence of augmented Lagrange multipliers for cone constrained optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 243-260, February.
- Regina Burachik & Alfredo Iusem & Jefferson Melo, 2010. "A primal dual modified subgradient algorithm with sharp Lagrangian," Journal of Global Optimization, Springer, vol. 46(3), pages 347-361, March.
- R. S. Burachik & A. N. Iusem & J. G. Melo, 2010. "Duality and Exact Penalization for General Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 125-140, October.
- Gulcin Dinc Yalcin & Refail Kasimbeyli, 2020. "On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 199-228, August.
- C. Y. Wang & X. Q. Yang & X. M. Yang, 2013. "Nonlinear Augmented Lagrangian and Duality Theory," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 740-760, November.
- Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
- Casey Rothschild & Florian Scheuer, 2014.
"A Theory of Income Taxation under Multidimensional Skill Heterogeneity,"
NBER Working Papers
19822, National Bureau of Economic Research, Inc.
- Casey Rothschild & Florian Scheuer, 2015. "A Theory of Income Taxation under Multidimensional Skill Heterogeneity," CESifo Working Paper Series 5165, CESifo.
- Casey Rothschild & Florian Scheuer, 2014. "A Theory of Income Taxation under Multidimensional Skill Heterogeneity," STICERD - Public Economics Programme Discussion Papers 19, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Rothschild, Casey & Scheuer, Florian, 2014. "A theory of income taxation under multidimensional skill heterogeneity," LSE Research Online Documents on Economics 58026, London School of Economics and Political Science, LSE Library.
- X. X. Huang & X. Q. Yang & K. L. Teo, 2007. "Lower-Order Penalization Approach to Nonlinear Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 1-20, January.
- Enrico Bellino, 2010. "Comment To ‘Commodity Content . . .’ By Fujimoto And Opocher," Metroeconomica, Wiley Blackwell, vol. 61(4), pages 749-753, November.
- D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
More about this item
Keywords
Valley-at-0 augmented Lagrangian function; Zero duality gap; Exact penalty function; Reflexive Banach space;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9455-6. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.