On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problems on Riemannian manifolds

Bilevel programming problems are often reformulated using the Karush-Kuhn-Tucker conditions for lower level problem resulting in a mathematical program with complementarity constraints (MPCC). First, we present KKT reformulation of bilevel optimization on Riemannian manifolds. Moreover, show that global optimal solutions theMPCCcorrespond to manifolds provided convex satisfies Slater?s constraint qualification. But relationship between local and its corresponding MPCC is incomplete equivalent. We then also by examples these correspondences can fail if qualification fails hold at lower-level problem. In addition,M- C-type optimality given.