Inexact Restoration Methods for Semivectorial Bilevel Programming Problem on Riemannian Manifolds

Jiagen Liao, Zhongping Wan
2022 Axioms  
For a better understanding of the bilevel programming on Riemannian manifolds, a semivectorial bilevel programming scheme is proposed in this paper. The semivectorial bilevel programming is firstly transformed into a single-level programming problem by using the Karush–Kuhn–Tucker (KKT) conditions of the lower-level problem, which is convex and satisfies the Slater constraint qualification. Then, the single-level programming is divided into two stages: restoration and minimization, based on
more » ... h an Inexact Restoration algorithm is developed. Under certain conditions, the stability and convergence of the algorithm are analyzed.
doi:10.3390/axioms11120696 fatcat:ex2goj4wmjdavegfnilxgiztdm