Reference : Accelerating the DC algorithm for smooth functions
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/26848
Accelerating the DC algorithm for smooth functions
English
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Fleming, Ronan MT mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Phan, Vuong mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
2015
Yes
[en] DC function, DC programming, DC algorithm, Łojasiewicz property, biochemical reaction networks
[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.
Department of Energy, Offices of Ad vanced Scientific Computing
Researchers
http://hdl.handle.net/10993/26848
http://arxiv.org/pdf/1507.07375v1.pdf
http://arxiv.org/abs/1507.07375

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