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Original Articles

Two Types of Approximate Saddle Points

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Pages 532-550 | Published online: 04 Jun 2008

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Balendu Bhooshan Upadhyay, Savin Treanţă & Priyanka Mishra. (2023) On Minty variational principle for nonsmooth multiobjective optimization problems on Hadamard manifolds. Optimization 72:12, pages 3081-3100.
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Xiang-Kai Sun, Kok Lay Teo & Xian-Jun Long. (2021) Characterizations of robust ε-quasi optimal solutions for nonsmooth optimization problems with uncertain data. Optimization 70:4, pages 847-870.
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M. Fakhar, M.R. Mahyarinia & J. Zafarani. (2019) On approximate solutions for nonsmooth robust multiobjective optimization problems. Optimization 68:9, pages 1653-1683.
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M. Golestani, H. Sadeghi & Y. Tavan. (2017) Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems. Numerical Functional Analysis and Optimization 38:6, pages 683-704.
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X.K. Sun & S.J. Li. (2013) Duality and gap function for generalized multivalued ϵ-vector variational inequality. Applicable Analysis 92:3, pages 482-492.
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Articles from other publishers (27)

Maryam Saadati & Morteza Oveisiha. (2024) Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications. Positivity 28:2.
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L. Huerga, B. Jiménez & V. Novo. 2023. Functional Analysis and Continuous Optimization. Functional Analysis and Continuous Optimization 195 211 .
C. Gutiérrez, R. López & J. Martínez. (2021) Generalized $${\varepsilon }$$-quasi solutions of set optimization problems. Journal of Global Optimization 82:3, pages 559-576.
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Savin Treanţă, Priyanka Mishra & Balendu Bhooshan Upadhyay. (2022) Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds. Mathematics 10:3, pages 523.
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Faizan A. Khan, Rohit K. Bhardwaj, Tirth Ram & Mohammed A. S. Tom. (2022) On approximate vector variational inequalities and vector optimization problem using convexificator. AIMS Mathematics 7:10, pages 18870-18882.
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L. Huerga, B. Jiménez, D. T. Luc & V. Novo. (2020) A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization. Mathematical Programming 189:1-2, pages 379-407.
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B. B. Upadhyay & Priyanka Mishra. 2021. Mathematical Analysis and Computing. Mathematical Analysis and Computing 443 458 .
Balendu Bhooshan Upadhyay & Priyanka Mishra. 2021. Optimization, Variational Analysis and Applications. Optimization, Variational Analysis and Applications 265 282 .
B. B. Upadhyay & Priyanka Mishra. 2021. Computational Management. Computational Management 325 343 .
Balendu Bhooshan Upadhyay, Priyanka Mishra, Ram N. Mohapatra & Shashi Kant Mishra. 2020. Optimization of Complex Systems: Theory, Models, Algorithms and Applications. Optimization of Complex Systems: Theory, Models, Algorithms and Applications 660 671 .
M. Golestani, H. Sadeghi & Y. Tavan. (2017) Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency. Journal of Optimization Theory and Applications 179:3, pages 896-916.
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M. X. You & S. J. Li. (2017) Nonlinear separation concerning E-optimal solution of constrained multi-objective optimization problems. Optimization Letters 12:1, pages 123-136.
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Zhen Wang, Ru Li & Guolin Yu. (2017) Vector critical points and generalized quasi-efficient solutions in nonsmooth multi-objective programming. Journal of Inequalities and Applications 2017:1.
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K. Das & C. Nahak. (2016) Approximate quasi efficiency of set-valued optimization problems via weak subdifferential. SeMA Journal 74:4, pages 523-542.
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K. Das & C. Nahak. (2016) Optimality conditions for approximate quasi efficiency in set-valued equilibrium problems. SeMA Journal 73:2, pages 183-199.
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Thai Doan Chuong & Do Sang Kim. (2015) Approximate solutions of multiobjective optimization problems. Positivity 20:1, pages 187-207.
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C. Gutiérrez, B. Jiménez & V. Novo. (2013) Optimality Conditions for Quasi-Solutions of Vector Optimization Problems. Journal of Optimization Theory and Applications 167:3, pages 796-820.
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Rui-Xue Yue & Ying Gao. (2015) Scalarizations for Approximate Quasi Efficient Solutions in Multiobjective Optimization Problems. Journal of the Operations Research Society of China 3:1, pages 69-80.
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Ying Gao, Xinmin Yang, Jin Yang & Hong Yan. (2015) Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps. Journal of Industrial & Management Optimization 11:2, pages 673-683.
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Lu Wei-zhong, Huang Shou-jun & Yang Jun. (2014) Optimality Conditions for ε -Vector Equilibrium Problems . Abstract and Applied Analysis 2014, pages 1-4.
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S. K. Mishra & B. B. Upadhyay. (2013) Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency. Positivity 17:4, pages 1071-1083.
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C. Gutiérrez, L. Huerga & V. Novo. (2012) Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems. Journal of Mathematical Analysis and Applications 389:2, pages 1046-1058.
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Hong-Yong Fu, Bin Dan & Xiang-Yu Liu. (2012) Existence and Duality of Generalized ε-Vector Equilibrium Problems. Journal of Applied Mathematics 2012, pages 1-13.
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Y. Gao, S. H. Hou & X. M. Yang. (2011) Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems. Journal of Optimization Theory and Applications 152:1, pages 97-120.
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Ying Gao, Xinmin Yang & Kok Lay Teo. (2011) Optimality conditions for approximate solutions of vector optimization problems. Journal of Industrial & Management Optimization 7:2, pages 483-496.
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C. Gutiérrez, R. López & V. Novo. (2010) Generalized -quasi-solutions in multiobjective optimization problems: Existence results and optimality conditions. Nonlinear Analysis: Theory, Methods & Applications 72:11, pages 4331-4346.
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Ying Gao, Xinmin Yang & HeungWingJoseph Lee. (2010) Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems. Journal of Inequalities and Applications 2010:1, pages 620928.
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