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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 64, 2015 - Issue 4
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Articles

E-Benson proper efficiency in vector optimization

Ke Quan ZhaoDepartment of Mathematics, Chongqing Normal University, Chongqing, China.Correspondence[email protected]
&
Xin Min YangDepartment of Mathematics, Chongqing Normal University, Chongqing, China.
Pages 739-752 | Received 07 Aug 2012, Accepted 11 Apr 2013, Published online: 06 Jun 2013

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Read on this site (5)

Yu Han. (2023) Density and connectedness of optimal points with respect to improvement sets. Optimization 72:4, pages 979-1008.
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Yang Dong Xu, Cheng Yu Lei & Chun Yu Sun. (2021) Nonlinear separation methods and applications for vector equilibrium problems using improvement sets. Applicable Analysis 100:15, pages 3182-3198.
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M. Ghaznavi, F. Akbari & E. Khorram. (2021) Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization. Optimization Methods and Software 36:2-3, pages 627-652.
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Chun-Rong Chen, Xin Zuo, Fang Lu & Sheng-Jie Li. (2016) Vector equilibrium problems under improvement sets and linear scalarization with stability applications. Optimization Methods and Software 31:6, pages 1240-1257.
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Kequan Zhao, Guangya Chen & Xinmin Yang. (2015) Approximate proper efficiency in vector optimization. Optimization 64:8, pages 1777-1793.
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Articles from other publishers (26)

Yu Han & Ke Quan Zhao. (2023) Stability of Optimal Points with Respect to Improvement Sets. Journal of Optimization Theory and Applications 199:3, pages 904-930.
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Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2023) Improvement Sets and Robust Multiobjective Optimization. Journal of the Operations Research Society of China.
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Liu Caiping & Yang Xinmin. (2023) bmE-properly efficient elements of vector optimization problems and their scalarization. SCIENTIA SINICA Mathematica.
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Zhou Zhiang, Chen Wang & Yu Guolin. (2023) Lower semicontinuity of the 解 maps of unified parametric generalized set-valued equilibrium problems with the improvement sets. SCIENTIA SINICA Mathematica 53:7, pages 1025.
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Quốc Anh Lâm, Thanh Dược Phạm, Thị Mộng Thúy Võ & Thị Mỹ Vân Đặng. (2023) Sự tồn tại nghiệm của bài toán tối ưu vector thông qua tập co-radiant. Can Tho University Journal of Science 59:Education in the Mekong Delta, pages 26-33.
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Zhi-Ang Zhou & Min Kuang. (2022) Scalarization and Optimality Conditions of E -Globally Proper Efficient Solution for Set-Valued Equilibrium Problems . Asia-Pacific Journal of Operational Research 40:02.
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Narges Hoseinpoor & Mehrdad Ghaznavi. (2023) Identifying approximate proper efficiency in an infinite dimensional space. RAIRO - Operations Research 57:2, pages 697-714.
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Vo Viet Tri. (2023) On equilibrium multivalued problems in the general model with the Boolean-valued bifunction. Numerical Algebra, Control and Optimization 0:0, pages 0-0.
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Quốc Anh Lâm, Thanh Dược Phạm, Thị Mộng Thúy Võ & Thị Mỹ Vân Đặng. (2022) Tính liên tục Hausdorff của ánh xạ nghiệm hữu hiệu yếu cho bài toán tối ưu vector phụ thuộc tham số thông qua tập cải tiến. Can Tho University Journal of Science 58:Education in the Mekong Delta, pages 19-25.
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Yuan-mei Xia, Xin-min Yang & Ke-quan Zhao. (2021) A combined scalarization method for multi-objective optimization problems. Journal of Industrial & Management Optimization 17:5, pages 2669.
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Hongwei Liang, Zhongping Wan & Litao Zhang. (2020) The connectedness of the solutions set for set-valued vector equilibrium problems under improvement sets. Journal of Inequalities and Applications 2020:1.
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Zhiang Zhou, Wang Chen & Xinmin Yang. (2019) Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis. Journal of Optimization Theory and Applications 183:3, pages 944-962.
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Ying Gao & Xin-Min Yang. (2018) Properties of the nonlinear scalar functional and its applications to vector optimization problems. Journal of Global Optimization 73:4, pages 869-889.
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Hui Guo & Yan-Qin Bai. (2018) A Kind of Unified Strict Efficiency via Improvement Sets in Vector Optimization. Journal of the Operations Research Society of China 6:4, pages 557-569.
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E. A. Youness & Mamdouh E. Elbrolosy. (2017) Extensions of proper efficiency in complex space. Mathematical Methods in the Applied Sciences 41:15, pages 5792-5800.
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Jiawei Chen, La Huang & Shengjie Li. (2018) Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets. Journal of Optimization Theory and Applications 178:3, pages 794-823.
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Hui Guo & Wan-li Zhang. (2016) Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems. Journal of the Operations Research Society of China 5:3, pages 419-430.
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Chun Hong Yuan & Wei Dong Rong. (2017) ? -Properly Efficiency of Multiobjective Semidefinite Programming with Set-Valued Functions . Mathematical Problems in Engineering 2017, pages 1-7.
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Yuan Mei Xia, Wan Li Zhang & Ke Quan Zhao. (2015) Characterizations of improvement sets via quasi interior and applications in vector optimization. Optimization Letters 10:4, pages 769-780.
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?? ?. (2016) E-Henig Proper Efficient Solution for Set-Valued Optimization Problems. Advances in Applied Mathematics 05:03, pages 494-504.
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Zhiang Zhou, Xinmin Yang & Kequan Zhao. (2015) $E$-super efficiency of set-valued optimization problems involving improvement sets. Journal of Industrial and Management Optimization 12:3, pages 1031-1039.
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Ke-Quan Zhao, Yuan-Mei Xia & Xin-Min Yang. (2015) NONLINEAR SCALARIZATION CHARACTERIZATIONS OF $E$-EFFICIENCY IN VECTOR OPTIMIZATION. Taiwanese Journal of Mathematics 19:2.
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Ke-Quan Zhao & Xin-Min Yang. (2014) $E$-PROPER SADDLE POINTS AND $E$-PROPER DUALITY IN VECTOR OPTIMIZATION WITH SET-VALUED MAPS. Taiwanese Journal of Mathematics 18:2.
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Ke Quan Zhao, Yuan Mei Xia & Hui Guo. (2014) A Characterization of -Benson Proper Efficiency via Nonlinear Scalarization in Vector Optimization . Journal of Applied Mathematics 2014, pages 1-5.
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Ke Quan Zhao & Yuan Mei Xia. (2014) A Kind of Unified Proper Efficiency in Vector Optimization. Abstract and Applied Analysis 2014, pages 1-5.
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Kequan Zhao & Xinmin Yang. (2013) Characterizations of the $E$-Benson proper efficiency in vector optimization problems. Numerical Algebra, Control & Optimization 3:4, pages 643-653.
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