Characterization of set relations through extensions of the oriented distance
Author
Abstract
Suggested Citation
DOI: 10.1007/s00186-019-00661-1
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Frank Heyde & Andreas Löhne & Christiane Tammer, 2009. "Set-valued duality theory for multiple objective linear programs and application to mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 159-179, March.
- Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
- Takashi Maeda, 2012. "On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 263-279, May.
- E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
- J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Marius Durea & Radu Strugariu, 2023. "Directional derivatives and subdifferentials for set-valued maps applied to set optimization," Journal of Global Optimization, Springer, vol. 85(3), pages 687-707, March.
- Elisa Caprari & Lorenzo Cerboni Baiardi & Elena Molho, 2022. "Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach," Journal of Global Optimization, Springer, vol. 84(2), pages 295-320, October.
- Zi-Ru Zhang & Yang-Dong Xu, 2024. "The Continuity and Convexity of a Nonlinear Scalarization Function with Applications in Set Optimization Problems Involving a Partial Order Relation," Mathematics, MDPI, vol. 12(23), pages 1-22, December.
- L. Huerga & B. Jiménez & V. Novo, 2022. "New Notions of Proper Efficiency in Set Optimization with the Set Criterion," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 878-902, December.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Khushboo & C. S. Lalitha, 2018. "Scalarizations for a unified vector optimization problem based on order representing and order preserving properties," Journal of Global Optimization, Springer, vol. 70(4), pages 903-916, April.
- Rocca Matteo & Papalia Melania, 2008. "Well-posedness in vector optimization and scalarization results," Economics and Quantitative Methods qf0807, Department of Economics, University of Insubria.
- S. J. Li & Y. D. Xu & S. K. Zhu, 2012. "Nonlinear Separation Approach to Constrained Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 842-856, September.
- Giovanni Paolo Crespi & Andreas H. Hamel & Matteo Rocca & Carola Schrage, 2021. "Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 361-381, February.
- Y. D. Xu & S. J. Li, 2013. "Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 663-684, June.
- L. Huerga & B. Jiménez & V. Novo & A. Vílchez, 2021. "Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 413-436, April.
- Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2004. "Isolated minimizers, proper efficiency and stability for C0,1 constrained vector optimization problems," Economics and Quantitative Methods qf0404, Department of Economics, University of Insubria.
- Onetti Alberto & Verma Sameer, 2008. "Licensing and Business Models," Economics and Quantitative Methods qf0806, Department of Economics, University of Insubria.
- Xu, Y.D. & Li, S.J. & Teo, K.L., 2012. "Vector network equilibrium problems with capacity constraints of arcs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 567-577.
- Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "From scalar to vector optimization," Economics and Quantitative Methods qf0305, Department of Economics, University of Insubria.
- Masamichi Kon, 2020. "A scalarization method for fuzzy set optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 135-152, June.
- Miglierina Enrico & Molho Elena & Rocca Matteo, 2004. "Well-posedness and scalarization in vector optimization," Economics and Quantitative Methods qf0403, Department of Economics, University of Insubria.
- Marius Durea & Radu Strugariu & Christiane Tammer, 2013. "Scalarization in Geometric and Functional Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 635-655, December.
- Radu Boţ & Sorin-Mihai Grad & Gert Wanka, 2007. "A general approach for studying duality in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 417-444, June.
- C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability for Properly Quasiconvex Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 492-506, November.
- Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022.
"Nonsmooth Implicit Differentiation for Machine Learning and Optimization,"
TSE Working Papers
22-1314, Toulouse School of Economics (TSE).
- Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022. "Nonsmooth Implicit Differentiation for Machine Learning and Optimization," TSE Working Papers 126768, Toulouse School of Economics (TSE).
- Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "First-Order Conditions for C0,1 Constrained vector optimization," Economics and Quantitative Methods qf0307, Department of Economics, University of Insubria.
- 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, Springer, vol. 186(2), pages 459-479, August.
- S. W. Xiang & W. S. Yin, 2007. "Stability Results for Efficient Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 385-398, September.
- S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 763-782, June.
More about this item
Keywords
Set optimization; Scalarization; Set order relations; Lower set less order; Oriented distance;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-019-00661-1. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.