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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 10: Variational Inequalities, Optimization and Related Topics
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Original Articles

Nonlinear separation in the image space with applications to penalty methods

Giandomenico Mastroeni Department of Mathematics, University of Pisa, Largo B. Pontecorvo, 5, 56100 Pisa, ItalyCorrespondence[email protected]
Pages 1901-1914 | Received 30 Jun 2011, Accepted 06 Aug 2011, Published online: 14 Sep 2011

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Y. D. Xu, P. P. Zhang & S. K. Zhu. (2021) Optimality conditions for efficient solutions of nonconvex constrained multiobjective optimization problems via image space analysis. Optimization 70:8, pages 1673-1701.
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Genghua Li & Shengjie Li. (2020) Optimality conditions for vector optimization problems with non-cone constraints in image space. Applicable Analysis 99:4, pages 611-626.
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Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2020) Characterizations of multiobjective robustness on vectorization counterparts. Optimization 69:3, pages 493-518.
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M. V. Dolgopolik. (2017) A unifying theory of exactness of linear penalty functions II: parametric penalty functions. Optimization 66:10, pages 1577-1622.
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Y. D. Xu. (2016) Nonlinear separation approach to inverse variational inequalities. Optimization 65:7, pages 1315-1335.
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Articles from other publishers (19)

Xiaoqing Ou, Suliman Al-Homidan, Qamrul Hasan Ansari & Jiawei Chen. (2023) Image space analysis for uncertain multiobjective optimization problems: Robust optimality conditions. Journal of Industrial and Management Optimization 19:1, pages 629.
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Manxue You & Shengjie Li. (2022) Perturbation of Image and conjugate duality for vector optimization. Journal of Industrial & Management Optimization 18:2, pages 731.
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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 191:1, pages 311-343.
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Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2020) Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis. Journal of Optimization Theory and Applications 186:2, pages 459-479.
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Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2019) A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems. Journal of Optimization Theory and Applications 184:2, pages 466-493.
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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 177:3, pages 788-810.
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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 177:3, pages 835-856.
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Shengjie Li, Yangdong Xu, Manxue You & Shengkun Zhu. (2018) Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization. Journal of Optimization Theory and Applications 177:3, pages 637-659.
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Shengkun Zhu. (2016) Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications. Journal of Optimization Theory and Applications 177:3, pages 743-769.
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Manxue You & Shengjie Li. (2016) Separation Functions and Optimality Conditions in Vector Optimization. Journal of Optimization Theory and Applications 175:2, pages 527-544.
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M. Chinaie & J. Zafarani. (2016) Nonlinear separation in the image space with applications to constrained optimization. Positivity 21:3, pages 1031-1047.
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Y. D. Xu. (2015) Nonlinear separation functions, optimality conditions and error bounds for Ky Fan quasi-inequalities. Optimization Letters 10:3, pages 527-542.
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Hezhi Luo, Huixian Wu & Jianzhen Liu. (2014) On Saddle Points in Semidefinite Optimization via Separation Scheme. Journal of Optimization Theory and Applications 165:1, pages 113-150.
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H. X. Wu, H. Z. Luo & J. F. Yang. (2013) Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming. Journal of Global Optimization 59:4, pages 695-727.
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S. K. Zhu & S. J. Li. (2013) Unified Duality Theory for Constrained Extremum Problems. Part I: Image Space Analysis. Journal of Optimization Theory and Applications 161:3, pages 738-762.
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S. K. Zhu & S. J. Li. (2013) Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes. Journal of Optimization Theory and Applications 161:3, pages 763-782.
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Y. D. Xu & S. J. Li. (2013) Nonlinear separation functions and constrained extremum problems. Optimization Letters 8:3, pages 1149-1160.
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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 159:2, pages 360-385.
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Y. D. Xu & S. J. Li. (2012) Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications. Journal of Optimization Theory and Applications 157:3, pages 663-684.
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