Geodesic
On the Karush-Kuhn-tucker reformulation of the bilevel optimization problems on Riemannian manifolds
Filomat, Tome 36 (2022) no. 11, p. 3609

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DOI

Bilevel programming problems are often reformulated using the Karush-Kuhn-Tucker conditions for the lower level problem resulting in a mathematical program with complementarity constraints (MPCC). First, we present KKT reformulation of the bilevel optimization problems on Riemannian manifolds. Moreover, we show that global optimal solutions of the MPCC correspond to global optimal solutions of the bilevel problem on the Riemannian manifolds provided the lower level convex problem satisfies the Slater's constraint qualification. But the relationship between the local solutions of the bilevel problem and its corresponding MPCC is incomplete equivalent. We then also show by examples that these correspondences can fail if the Slater's constraint qualification fails to hold at lower-level convex problem. In addition, M-and C-type optimality conditions for the bilevel problem on Riemannian manifolds are given.
DOI : 10.2298/FIL2211609L
Classification : 26B25, 90C26
Keywords: Bilevel optimization problem, KKT reformulation, Riemannian manifolds, optimality conditions 
Jiagen Liao; Zhongping Wan. On the Karush-Kuhn-tucker reformulation of the bilevel optimization problems on Riemannian manifolds. Filomat, Tome 36 (2022) no. 11, p. 3609 . doi: 10.2298/FIL2211609L
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     author = {Jiagen Liao and Zhongping Wan},
     title = {On the {Karush-Kuhn-tucker} reformulation of the bilevel optimization problems on {Riemannian} manifolds},
     journal = {Filomat},
     pages = {3609 },
     year = {2022},
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     doi = {10.2298/FIL2211609L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2211609L/}
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