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Keywords = semivectorial bilevel programming

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17 pages, 316 KB  
Article
Inexact Restoration Methods for Semivectorial Bilevel Programming Problem on Riemannian Manifolds
by Jiagen Liao and Zhongping Wan
Axioms 2022, 11(12), 696; https://doi.org/10.3390/axioms11120696 - 5 Dec 2022
Cited by 2 | Viewed by 1771
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Analysis)
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