Fuzzy and Exact Necessary Optimality Conditions for a Nonsmooth Bilevel Semi-Infinite Program
Keywords:
Parametric optimization, semi-infinite programming, optimality conditions, marginal and value functions, generalized differentiation, bilevel programming.Abstract
We investigate the so-called nonsmooth bilevel semi-infinite programming problem when the involved functions are nonconvex. This type of problems consists of an infinite number of constraints with arbitrary index sets. To establish the optimality conditions, we rewrite upper estimates of three recently developed subdifferentials of the value functions using two new qualification conditions (CQs), which are weaker than the existing Mangasarian-Fromovitz and Farkas-Minkowski CQs. We point out that the obtained results are new if we take up a finite number of constraints as well.
Downloads
Downloads
Published
Issue
Section
License
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- 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.
- 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.
