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 a 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 non-smooth 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 non-expansive operator in an infinite dimensional Hilbert space. Then we convert the simple bilevel optimization problem to a fixed-point problem of a non-expansive 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
1-19
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
1 January 2021
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), .
(doi:10.1080/10556788.2019.1619729).
Abstract
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as a 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 non-smooth 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 non-expansive operator in an infinite dimensional Hilbert space. Then we convert the simple bilevel optimization problem to a fixed-point problem of a non-expansive 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.
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An inertial extrapolation method for convex simple bilevel optimization
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Accepted/In Press date: 10 May 2019
e-pub ahead of print date: 27 May 2019
Published date: 1 January 2021
Additional Information:
Funding Information:
The work of Phan Tu Vuong is funded by the Austrian Science Fund (FWF) project number M2499-N32. The work of Alain Zemkoho is funded by the EPSRC Grant EP/P022553/1. The research of Yekini Shehu is supported by the Alexander von Humbold-Foundation and Postdoctoral Fellowship Grant from the Institute of Science and Technology, Klosterneuburg, Vienna, Austria. The authors are indebted to two anonymous referees for their constructive remarks, which have helped us to improve the quality of the paper. We would also like to thank the Associate Editor for the efficient handling of the review process.
Publisher Copyright:
© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
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
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Date deposited: 19 Sep 2018 16:30
Last modified: 16 Mar 2024 07:05
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Yekini Shehu
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