Inexact Restoration Methods for Semivectorial Bilevel Programming Problem on Riemannian Manifolds

Author:

Liao JiagenORCID,Wan Zhongping

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

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference29 articles.

1. Udrişte, C. (2013). Convex Functions and Optimization Methods on Riemannian Manifolds, Springer Science & Business Media.

2. Boumal, N. (2020, September 11). An Introduction to Optimization on Smooth Manifolds. Available online: https://www.nicolasboumal.net/book/.

3. Liao, L., and Wan, Z. (Filomat, 2022). On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problems on Riemannian manifolds, Filomat, accepted and in press .

4. Inexact-restoration algorithms for constrained optimization;Pilotta;J. Optim. Theory Appl.,2000

5. Inexact-restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming;J. Optim. Theory Appl.,2001

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