Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 66, 2017 - Issue 1
399
Views
42
CrossRef citations to date
0
Altmetric
Articles

Well-posedness and stability of solutions for set optimization problems

&
Pages 17-33 | Received 13 May 2016, Accepted 05 Oct 2016, Published online: 20 Oct 2016

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (12)

Monica Burlică, Marius Durea & Radu Strugariu. (2023) New concepts of directional derivatives for set-valued maps and applications to set optimization. Optimization 72:4, pages 1069-1091.
Read now
Michel H. Geoffroy & James Larrouy. (2022) A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization. Numerical Functional Analysis and Optimization 43:16, pages 1848-1883.
Read now
Karuna & C. S. Lalitha. (2022) Essential stability in set optimization. Optimization 71:7, pages 1803-1816.
Read now
Mihaela Miholca. (2021) Global Well-Posedness in Set Optimization. Numerical Functional Analysis and Optimization 42:14, pages 1700-1717.
Read now
Chuang-liang Zhang & Nan-jing Huang. (2021) On the stability of minimal solutions for parametric set optimization problems. Applicable Analysis 100:7, pages 1533-1543.
Read now
Jia-yu Mao, San-hua Wang & Yu Han. (2019) The stability of the solution sets for set optimization problems via improvement sets. Optimization 68:11, pages 2171-2193.
Read now
Yu Han. (2019) Nonlinear scalarizing functions in set optimization problems. Optimization 68:9, pages 1685-1718.
Read now
Karuna & C. S. Lalitha. (2019) External and internal stability in set optimization. Optimization 68:4, pages 833-852.
Read now

Articles from other publishers (30)

Manli Yang, Taiyong Li & Guanghui Xu. (2024) Continuity of the solutions sets for parametric set optimization problems. Journal of Inequalities and Applications 2024:1.
Crossref
Meenakshi Gupta & Manjari Srivastava. (2024) Hadamard well-posedness and stability in set optimization. Positivity 28:1.
Crossref
Zai-Yun Peng, Chong-Yang Shao, Yue Zeng & Yi-Bin Xiao. (2024) Painlevé–Kuratowski Stability of Approximate Solution Sets for Perturbed Set Optimization Problems Under General Ordering Sets by Recession Cone. Taiwanese Journal of Mathematics -1:-1.
Crossref
Zai-Yun Peng, Xue-Jing Chen, Yun-Bin Zhao & Xiao-Bing Li. (2022) Painlevé-Kuratowski convergence of minimal solutions for set-valued optimization problems via improvement sets. Journal of Global Optimization 87:2-4, pages 759-781.
Crossref
Tran Quoc Duy & Vo Si Trong Long. (2023) On global well-posedness of semi-infinite set optimization problems. Computational and Applied Mathematics 42:6.
Crossref
Pradeep Kumar Sharma & C. S. Lalitha. (2022) Connectedness of the solution sets in generalized semi-infinite set optimization. Optimization Letters 17:7, pages 1575-1594.
Crossref
Chuang-liang Zhang, Nan-jing Huang & Donal O'Regan. (2023) Stability of solutions for fuzzy set optimization problems with applications. Fuzzy Sets and Systems 466, pages 108470.
Crossref
Taiyong Li & Yanhui Wei. (2023) The stability of minimal solution sets for set optimization problems via improvement sets. Journal of Inequalities and Applications 2023:1.
Crossref
Kuntal Som & V. Vetrivel. (2022) Pointwise well-posedness of a set-valued optimization problem at a weak solution. The Journal of Analysis 31:1, pages 187-199.
Crossref
Marius Durea & Radu Strugariu. (2022) Directional derivatives and subdifferentials for set-valued maps applied to set optimization. Journal of Global Optimization 85:3, pages 687-707.
Crossref
Kuntal Som & V. Vetrivel. (2022) Global well-posedness of set-valued optimization with application to uncertain problems. Journal of Global Optimization 85:2, pages 511-539.
Crossref
Karuna & C. S. Lalitha. (2022) Convergence, Scalarization and Continuity of Minimal Solutions in Set Optimization. Journal of the Operations Research Society of China.
Crossref
Mihaela Miholca. (2022) Well-posedness for set-valued equilibrium problems. Studia Universitatis Babes-Bolyai Matematica 67:1, pages 91-103.
Crossref
Khushboo & C.S. Lalitha. (2021) Scalarization and convergence in unified set optimization. RAIRO - Operations Research 55:6, pages 3603-3616.
Crossref
Tran Quoc Duy. (2021) Levitin–Polyak well-posedness in set optimization concerning Pareto efficiency. Positivity 25:5, pages 1923-1942.
Crossref
Meenakshi Gupta & Manjari Srivastava. (2021) On Levitin–Polyak well-posedness and stability in set optimization. Positivity 25:5, pages 1903-1921.
Crossref
Chuang-liang Zhang & Nan-jing Huang. (2021) Well-posedness and stability in set optimization with applications. Positivity 25:3, pages 1153-1173.
Crossref
Chuang-liang Zhang & Nan-jing Huang. (2020) Set optimization problems of generalized semi-continuous set-valued maps with applications. Positivity 25:2, pages 353-367.
Crossref
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.
Crossref
Qamrul Hasan Ansari & Pradeep Kumar Sharma. 2021. Optimization, Variational Analysis and Applications. Optimization, Variational Analysis and Applications 103 165 .
Yu Han. (2020) Connectedness of weak minimal solution set for set optimization problems. Operations Research Letters 48:6, pages 820-826.
Crossref
L. Q. Anh, T. Q. Duy & D. V. Hien. (2020) Stability of efficient solutions to set optimization problems. Journal of Global Optimization 78:3, pages 563-580.
Crossref
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.
Crossref
Pham Thi Vui, Lam Quoc Anh & Rabian Wangkeeree. (2020) Well-Posedness for Set Optimization Problems Involving Set Order Relations. Acta Mathematica Vietnamica 45:2, pages 329-344.
Crossref
Lam Quoc Anh, Tran Quoc Duy, Dinh Vinh Hien, Daishi Kuroiwa & Narin Petrot. (2020) Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation. Journal of Optimization Theory and Applications 185:2, pages 416-432.
Crossref
Yu Han, Kai Zhang & Nan-jing Huang. (2019) The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence. Mathematical Methods of Operations Research 91:1, pages 175-196.
Crossref
Pham Thi Vui, Lam Quoc Anh & Rabian Wangkeeree. (2018) Levitin–Polyak well-posedness for set optimization problems involving set order relations. Positivity 23:3, pages 599-616.
Crossref
Yu Han, San-hua Wang & Nan-jing Huang. (2019) Arcwise connectedness of the solution sets for set optimization problems. Operations Research Letters 47:3, pages 168-172.
Crossref
Meenakshi Gupta & Manjari Srivastava. (2018) Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior. Journal of Global Optimization 73:2, pages 447-463.
Crossref
Yu Han & Nan-jing Huang. (2017) Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications. Journal of Optimization Theory and Applications 177:3, pages 679-695.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.