Accelerating the DC algorithm for smooth functions

Francisco J. Aragón Artacho, Ronan M. T. Fleming, Phan T. Vuong

Published 2015-07-27Version 1

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 {\L}ojasiewicz 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 {\L}ojasiewicz 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.