Abstract
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 which an Inexact Restoration algorithm is developed. Under certain conditions, the stability and convergence of the algorithm are analyzed.
Funder
Natural Science Foundation of China
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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