Accelerating the DC algorithm for smooth functions

• 成果类型: Article
• 署名作者: Aragon Artacho, Francisco J.; Fleming, Ronan M. T.; Vuong, Phan T.
• 署名单位: Universitat d'Alacant; University of Luxembourg
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1180-1
• 发表日期: 2018
• 页码: 95-118
• 关键词: minimizing composite functions; minimization; CONVERGENCE; nonconvex; reconstruction; models

摘要

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 Aojasiewicz 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 Aojasiewicz 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.