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Accelerating the DC algorithm for smooth functions
Aragón Artacho, Francisco Javier; Fleming, Ronan MT; Phan, Vuong
2015
 

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Keywords :
DC function, DC programming, DC algorithm, Łojasiewicz property, biochemical reaction networks
Abstract :
[en] 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 outperforms DCA, being on average more than four times faster in both computational time and the number of iterations. The algorithms are globally convergent to a non-equilibrium steady state of a biochemical network, with only chemically consistent restrictions on the network topology.
Disciplines :
Mathematics
Author, co-author :
Aragón Artacho, Francisco Javier ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Fleming, Ronan MT ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Phan, Vuong ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Language :
English
Title :
Accelerating the DC algorithm for smooth functions
Publication date :
2015
Focus Area :
Computational Sciences
Funders :
Department of Energy, Offices of Ad vanced Scientific Computing
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since 22 April 2016

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