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Accelerating the DC algorithm for smooth functions

Accelerating the DC algorithm for smooth functions
Accelerating the DC algorithm for smooth functions
We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the Łojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the Łojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperform DCA, being on average more than four times faster in both computational time and the number of iterations. Numerical experiments show that the algorithms are globally convergent to a non-equilibrium steady state of various biochemical networks, with only chemically consistent restrictions on the network topology.
0025-5610
95-118
Aragón Artacho, Francisco J.
27fd51f0-ca5f-4b38-86de-1b9c7eec8312
Fleming, Ronan M. T.
8ee22afd-fc39-4e83-9e1b-5078c9569ab8
Vuong, Phan T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Aragón Artacho, Francisco J.
27fd51f0-ca5f-4b38-86de-1b9c7eec8312
Fleming, Ronan M. T.
8ee22afd-fc39-4e83-9e1b-5078c9569ab8
Vuong, Phan T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Aragón Artacho, Francisco J., Fleming, Ronan M. T. and Vuong, Phan T. (2018) Accelerating the DC algorithm for smooth functions. Mathematical Programming, 169 (1), 95-118. (doi:10.1007/s10107-017-1180-1).

Record type: Article

Abstract

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the Łojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the Łojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperform DCA, being on average more than four times faster in both computational time and the number of iterations. Numerical experiments show that the algorithms are globally convergent to a non-equilibrium steady state of various biochemical networks, with only chemically consistent restrictions on the network topology.

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More information

Accepted/In Press date: 8 July 2017
e-pub ahead of print date: 17 July 2017
Published date: 1 May 2018

Identifiers

Local EPrints ID: 434861
URI: http://eprints.soton.ac.uk/id/eprint/434861
ISSN: 0025-5610
PURE UUID: 66be7d9a-7fc9-4d9c-817d-d4df718135e2
ORCID for Phan T. Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 11 Oct 2019 16:30
Last modified: 17 Dec 2019 01:20

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