Generalized Characterization Theorems for Set Relations and an Application to Multi-Valued Optimization

Authors

  • Yuto Ogata Author

Keywords:

Set optimization, set relation, scalarization, theorem of the alternative, robustness

Abstract

 This paper proposes relaxed characterization for set relations by scalarization functions and states a generalized Gordan’s theorem of the alternative for set-valued maps. As an application, we introduce some robustness of multi-valued optimization problems together with an algorithm by which its criteria can be calculated.

Downloads

Download data is not yet available.

Downloads

Published

2024-07-05

Issue

Vol. 9 No. 2 (2024): volume 9 issue 2 (2024)

Section

Articles

License

You are free to:

  1. Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
  2. Adapt — remix, transform, and build upon the material for any purpose, even commercially.
  3. The licensor cannot revoke these freedoms as long as you follow the license terms.

Under the following terms:

  1. Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  2. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Notices:

You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .

No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.

How to Cite

Generalized Characterization Theorems for Set Relations and an Application to Multi-Valued Optimization. (2024). Minimax Theory and Its Applications, 9(2), 377–388. https://journalmta.com/index.php/jmta/article/view/135