The main aim of this paper is to establish sufficient optimality conditions using an upper estimate of Clarke subdifferential of value function and the concept of convexifactor for optimistic bilevel programming problems with convex and non-convex lower-level problems. For this purpose, the notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are defined in terms of the convexifactors. 1. Introduction. Bilevel programming problem comprises of two optimization problems where the

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... riables of the first (or upper-level) problem are the parameters of the second (or lower-level) problem and the set of optimal solutions of the second problem is needed to calculate the objective function value of the first problem. It plays an important role not only in theoretical studies but also in practical applications. This motivated an intensive investigation of this problem by many mathematicians, economists and engineers. For applications and recent developments on the subject one can see Bard [2] and Dempe [7] . Development of optimality conditions for bilevel programming problems has been a challenging area for research community. Many researchers, including Bard [3, 4] , Dempe [8, 9] , Outrata [29], Ye and Zhu [35], Dempe et al. [10], Ye [33, 34], Suneja and Kohli [30], have worked in this direction. Recently, Kohli [21] has introduced two versions of nonsmooth Abadie constraint qualification (ACQ) in terms of convexifactor and Clarke subdifferential and employed the weaker version to develop Karush-Kuhn-Tucker (KKT) type necessary optimality conditions for an optimistic bilevel programming problem with convex and non-convex lower-level problems using an upper estimate of Clarke subdifferential of value function in variational analysis and the concept of convexifactor. Consider the following bilevel programming problem Kohli [21]: (BLPP) Minimize x,y F (x, y) subject to G j (x, y) ≤ 0, j ∈ J, y ∈ ψ(x), 2020 Mathematics Subject Classification. 90C26, 90C46.