The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

An inertial extrapolation method for convex simple bilevel optimization

An inertial extrapolation method for convex simple bilevel optimization
An inertial extrapolation method for convex simple bilevel optimization
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and nonsmooth functions while the outer one is the minimization of a smooth convex function. We first formulate and give strong convergence analysis of an inertial algorithm for fixed-point problem of a nonexpansive operator in an infinite dimensional Hilbert spaces. Then we convert the simple bilevel optimization problem to a fixed-point problem of a nonexpansive operator in finite dimensional space and design the corresponding algorithm and establish its convergence. Our numerical experiments show that the proposed method in this paper outperforms the currently known best algorithm to solve the class of bilevel optimization problem considered.
Simple bilevel optimization, fixed-point iterative method, inertial extrapolation
1055-6788
1-19
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Shehu, Yekini, Vuong, Phan Tu and Zemkoho, Alain (2021) An inertial extrapolation method for convex simple bilevel optimization. Optimization Methods and Software, 36 (1), 1-19. (doi:10.1080/10556788.2019.1619729).

Record type: Article

Abstract

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and nonsmooth functions while the outer one is the minimization of a smooth convex function. We first formulate and give strong convergence analysis of an inertial algorithm for fixed-point problem of a nonexpansive operator in an infinite dimensional Hilbert spaces. Then we convert the simple bilevel optimization problem to a fixed-point problem of a nonexpansive operator in finite dimensional space and design the corresponding algorithm and establish its convergence. Our numerical experiments show that the proposed method in this paper outperforms the currently known best algorithm to solve the class of bilevel optimization problem considered.

Text
arxiv version - Accepted Manuscript
Download (454kB)
Text
Main Document Final - Accepted Manuscript
Download (468kB)
Text
An inertial extrapolation method for convex simple bilevel optimization - Version of Record
Available under License Creative Commons Attribution.
Download (1MB)

More information

Accepted/In Press date: 10 May 2019
e-pub ahead of print date: 27 May 2019
Published date: 1 January 2021
Keywords: Simple bilevel optimization, fixed-point iterative method, inertial extrapolation

Identifiers

Local EPrints ID: 423168
URI: http://eprints.soton.ac.uk/id/eprint/423168
ISSN: 1055-6788
PURE UUID: 70678e2a-d254-4701-96bf-815d94fb05bf
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X
ORCID for Alain Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 19 Sep 2018 16:30
Last modified: 13 Nov 2021 05:20

Export record

Altmetrics

Contributors

Author: Yekini Shehu
Author: Phan Tu Vuong ORCID iD
Author: Alain Zemkoho ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×