On Approximate Variational Inequalities and Bilevel Programming Problems
Balendu Bhooshan Upadhyay,
Ioan Stancu-Minasian,
Subham Poddar
et al.
Abstract:In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local ϵ-quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan’s lemma, we derive some exis… Show more
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