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 [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) > >] | |

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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