Characterizations, dynamical systems and gradient methods for strongly quasiconvex functions
Characterizations, dynamical systems and gradient methods for strongly quasiconvex functions
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthermore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this for establishing exponential convergence for first- and second-order gradient systems without relying on the usual Lipschitz continuity assumption on the gradient of the function. The explicit discretization of the first-order dynamical system leads to the gradient descent method while discretization of the second-order dynamical system with viscous damping recovers the heavy ball method. We establish the linear convergence of both methods under suitable conditions on the parameters as well as numerical experiments for supporting our theoretical findings.
Lara, Felipe
57a91d3d-65d3-46b1-9ee5-f93c90dbcb5f
Marcavillaca, Raul T.
ef2642e4-53b7-47b0-be1f-951ee352dcc3
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Lara, Felipe
57a91d3d-65d3-46b1-9ee5-f93c90dbcb5f
Marcavillaca, Raul T.
ef2642e4-53b7-47b0-be1f-951ee352dcc3
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Lara, Felipe, Marcavillaca, Raul T. and Vuong, Phan Tu
(2025)
Characterizations, dynamical systems and gradient methods for strongly quasiconvex functions.
Journal of Optimization Theory and Applications, 206, [60].
(doi:10.1007/s10957-025-02728-y).
Abstract
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthermore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this for establishing exponential convergence for first- and second-order gradient systems without relying on the usual Lipschitz continuity assumption on the gradient of the function. The explicit discretization of the first-order dynamical system leads to the gradient descent method while discretization of the second-order dynamical system with viscous damping recovers the heavy ball method. We establish the linear convergence of both methods under suitable conditions on the parameters as well as numerical experiments for supporting our theoretical findings.
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s10957-025-02728-y
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Accepted/In Press date: 7 May 2025
e-pub ahead of print date: 11 June 2025
Identifiers
Local EPrints ID: 504515
URI: http://eprints.soton.ac.uk/id/eprint/504515
ISSN: 0022-3239
PURE UUID: dbab4694-0aa5-4cd5-a117-0cabe318a842
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Date deposited: 10 Sep 2025 15:56
Last modified: 11 Sep 2025 03:11
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Author:
Felipe Lara
Author:
Raul T. Marcavillaca
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