Separation Approach for Augmented Lagrangians in Constrained Nonconvex Optimization
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DOI: 10.1007/s10957-009-9598-0
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References listed on IDEAS
- D. Li & X. L. Sun, 2000. "Local Convexification of the Lagrangian Function in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 109-120, January.
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Cited by:
- Shengkun Zhu, 2018. "Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 743-769, June.
- Hezhi Luo & Huixian Wu & Jianzhen Liu, 2015. "On Saddle Points in Semidefinite Optimization via Separation Scheme," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 113-150, April.
- Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
- H. Wu & H. Luo & J. Yang, 2014. "Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 59(4), pages 695-727, August.
- M. V. Dolgopolik, 2018. "Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property," Journal of Global Optimization, Springer, vol. 71(2), pages 237-296, June.
- H. Luo & H. Wu & G. Chen, 2012. "On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 599-618, November.
- Shengkun Zhu, 2018. "Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part I: The Scalar Finite-Dimensional Case," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 770-787, June.
- Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.
- Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
- Hezhi Luo & Huixian Wu & Jianzhen Liu, 2013. "Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 360-385, November.
- Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "A Unified Characterization of Multiobjective Robustness via Separation," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 86-102, 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.
- 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.
- Letizia Pellegrini & Shengkun Zhu, 2018. "Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 788-810, June.
- H. Wu & H. Luo, 2012. "Saddle points of general augmented Lagrangians for constrained nonconvex optimization," Journal of Global Optimization, Springer, vol. 53(4), pages 683-697, August.
- Huixian Wu & Hezhi Luo & Xiaodong Ding & Guanting Chen, 2013. "Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(3), pages 531-558, December.
- 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.
- Manxue You & Shengjie Li, 2017. "Separation Functions and Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 527-544, November.
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Keywords
Image space analysis; Separation; Saddle points; Augmented Lagrangian function;All these keywords.
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