Sufficient Conditions and Duality Results in Bilevel Optimization Using Tangential Subdifferentials

The problem addressed in this paper involves a sequence of two optimization problems, where the feasible region of the upper-level problem is implicitly determined by the solution set of a parameterized lower-level problem, with all functions being tangentially convex at the considered point. Building on the recent work of Gadhi and Ohda [(2024). Applying tangential subdifferentials in bilevel optimization. Optimization, 73, 2919–2932, https://doi.org/10.1080/02331934.2023.2231501], which addressed necessary optimality conditions using tangential subdifferentials, we focus on deriving sufficient optimality conditions and establishing duality results. Our approach to achieving the first goal combines the optimal value reformulation with relatively Dini-generalized convexities, followed by an example to illustrate the resulting findings. To achieve the second goal, we introduce a Mond-Weir dual for the original bilevel optimization problem and subsequently establish both weak and strong duality results.