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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 10
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Articles

Treatment of set order relations by means of a nonlinear scalarization functional: a full characterization

Elisabeth KöbisFaculty of Natural Sciences II, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany.Correspondence[email protected]
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Markus A. KöbisFaculty of Natural Sciences II, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany.
Pages 1805-1827 | Received 15 Jun 2016, Accepted 22 Jul 2016, Published online: 10 Aug 2016

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Truong Xuan Duc Ha. (2024) A unified scheme for scalarization in set optimization. Optimization 73:5, pages 1645-1679.
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Zhiang Zhou, Min Huang & Elisabeth Köbis. (2024) Globally proper efficiency of set optimization problems based on the certainly set less order relation. Applicable Analysis 103:1, pages 184-197.
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Lam Quoc Anh, Pham Thanh Duoc & Tran Thi Thuy Duong. (2023) A new scalarization approach and applications in set optimization. Optimization 72:4, pages 1093-1117.
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Gabriele Eichfelder & Stefan Rocktäschel. (2023) Solving set-valued optimization problems using a multiobjective approach. Optimization 72:3, pages 789-820.
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B. Jiménez, V. Novo & A. Vílchez. (2020) Six set scalarizations based on the oriented distance: properties and application to set optimization. Optimization 69:3, pages 437-470.
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B. Jiménez, V. Novo & A. Vílchez. (2018) A set scalarization function based on the oriented distance and relations with other set scalarizations. Optimization 67:12, pages 2091-2116.
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Qamrul Hasan Ansari, Elisabeth Köbis & Pradeep Kumar Sharma. (2018) Characterizations of set relations with respect to variable domination structures via oriented distance function. Optimization 67:9, pages 1389-1407.
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Jiawei Chen, Qamrul Hasan Ansari & Jen-Chih Yao. (2017) Characterizations of set order relations and constrained set optimization problems via oriented distance function. Optimization 66:11, pages 1741-1754.
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Lam Quoc Anh & Tran Ngoc Tam. The use of a family of Gerstewitz scalarization functions in the context of vector optimization with variable domination structures to derive scalarization results. Optimization Methods and Software 0:0, pages 1-16.
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Articles from other publishers (24)

Madhusudan Das, Chandal Nahak & Mahendra Prasad Biswal. (2024) Treatment of Set-Valued Robustness via Separation and Scalarization. Journal of Optimization Theory and Applications.
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Anveksha Moar, Pradeep Kumar Sharma & C. S. Lalitha. (2024) Nonlinear scalarization in set optimization based on the concept of null set. Journal of Global Optimization.
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Yousuke Araya. (2023) Conjugate Duality in Set Optimization via Nonlinear Scalarization. Journal of Optimization Theory and Applications 199:2, pages 466-498.
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Khushboo & C. S. Lalitha. (2022) Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization. Journal of Global Optimization 85:1, pages 235-249.
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Elisa Caprari, Lorenzo Cerboni Baiardi & Elena Molho. (2022) Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach. Journal of Global Optimization 84:2, pages 295-320.
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Gabriele Eichfelder, Ernest Quintana & Stefan Rocktäschel. (2022) A Vectorization Scheme for Nonconvex Set Optimization Problems. SIAM Journal on Optimization 32:2, pages 1184-1209.
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Johannes Jahn. (2022) Characterizations of the Set Less Order Relation in Nonconvex Set Optimization. Journal of Optimization Theory and Applications 193:1-3, pages 523-544.
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Gemayqzel Bouza, Ernest Quintana & Christiane Tammer. (2021) A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality. Journal of Optimization Theory and Applications 190:3, pages 711-743.
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Lam Quoc Anh, Nguyen Huu Danh, Pham Thanh Duoc & Tran Ngoc Tam. (2021) Qualitative properties of solutions to set optimization problems. Computational and Applied Mathematics 40:2.
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Pei-Pei Liu, Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2018) Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods. Journal of the Operations Research Society of China 9:1, pages 79-97.
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Qamrul Hasan Ansari & Pradeep Kumar Sharma. 2021. Optimization, Variational Analysis and Applications. Optimization, Variational Analysis and Applications 103 165 .
Khushboo & C. S. Lalitha. 2021. Optimization, Variational Analysis and Applications. Optimization, Variational Analysis and Applications 1 17 .
Lam Quoc Anh, Nguyen Huu Danh & Tran Ngoc Tam. (2020) Continuity of Solution Maps to Parametric Set Optimization Problems via Parametric Equilibrium Problems. Acta Mathematica Vietnamica 45:2, pages 383-395.
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Gabriele Eichfelder, Julia Niebling & Stefan Rocktäschel. (2019) An algorithmic approach to multiobjective optimization with decision uncertainty. Journal of Global Optimization 77:1, pages 3-25.
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Qamrul Hasan Ansari, Andreas H Hamel & Pradeep Kumar Sharma. (2019) Ekeland’s variational principle with weighted set order relations. Mathematical Methods of Operations Research 91:1, pages 117-136.
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Truong Xuan Duc Ha. (2019) A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach. Mathematical Methods of Operations Research 91:1, pages 137-158.
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B. Jiménez, V. Novo & A. Vílchez. (2019) Characterization of set relations through extensions of the oriented distance. Mathematical Methods of Operations Research 91:1, pages 89-115.
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Elisabeth Köbis, Markus A. Köbis & Xiaolong Qin. (2020) An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces. Mathematics 8:1, pages 143.
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Elisabeth Köbis, Markus A. Köbis & Xiaolong Qin. (2019) Nonlinear Separation Approach to Inverse Variational Inequalities in Real Linear Spaces. Journal of Optimization Theory and Applications 183:1, pages 105-121.
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María Alonso, Elvira Hernández & Elena Pereira. (2018) Optimality conditions and minimax properties in set optimization. Optimization Letters 13:1, pages 55-68.
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Hong-Zhi Wei, Chun-Rong Chen & Sheng-Jie Li. (2017) A Unified Characterization of Multiobjective Robustness via Separation. Journal of Optimization Theory and Applications 179:1, pages 86-102.
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Elisabeth Köbis, Thanh Tam Le & Christiane Tammer. (2017) A Generalized Scalarization Method in Set Optimization with Respect to Variable Domination Structures. Vietnam Journal of Mathematics 46:1, pages 95-125.
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Petra Weidner. (2017) Construction of functions with uniform sublevel sets. Optimization Letters 12:1, pages 35-41.
Crossref
Gabriele Eichfelder & Maria Pilecka. 2018. Applications of Nonlinear Analysis. Applications of Nonlinear Analysis 265 304 .

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