Upadhyay, B.B.; Stancu-Minasian, I.M.; Poddar, S.; Mishra, P. On Approximate Variational Inequalities and Bilevel Programming Problems. Preprints2024, 2024040484. https://doi.org/10.20944/preprints202404.0484.v1
APA Style
Upadhyay, B.B., Stancu-Minasian, I.M., Poddar, S., & Mishra, P. (2024). On Approximate Variational Inequalities and Bilevel Programming Problems. Preprints. https://doi.org/10.20944/preprints202404.0484.v1
Chicago/Turabian Style
Upadhyay, B.B., Subham Poddar and Priyanka Mishra. 2024 "On Approximate Variational Inequalities and Bilevel Programming Problems" Preprints. https://doi.org/10.20944/preprints202404.0484.v1
Abstract
In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
