Accelerating the DC algorithm for smooth functions
Abstract
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 Lojasiewicz 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 Lojasiewicz 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.
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Luxembourg (Luxembourg)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER)
- OSTI Identifier:
- 1371487
- Alternate Identifier(s):
- OSTI ID: 1510489
- Grant/Contract Number:
- SC0010429
- Resource Type:
- Published Article
- Journal Name:
- Mathematical Programming
- Additional Journal Information:
- Journal Name: Mathematical Programming Journal Volume: 169 Journal Issue: 1; Journal ID: ISSN 0025-5610
- Publisher:
- Springer
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; DC function; DC programming; DC algorithm; Łojasiewicz property; Biochemical reaction networks
Citation Formats
Aragón Artacho, Francisco J., Fleming, Ronan M. T., and Vuong, Phan T. Accelerating the DC algorithm for smooth functions. Netherlands: N. p., 2017.
Web. doi:10.1007/s10107-017-1180-1.
Aragón Artacho, Francisco J., Fleming, Ronan M. T., & Vuong, Phan T. Accelerating the DC algorithm for smooth functions. Netherlands. https://doi.org/10.1007/s10107-017-1180-1
Aragón Artacho, Francisco J., Fleming, Ronan M. T., and Vuong, Phan T. Mon .
"Accelerating the DC algorithm for smooth functions". Netherlands. https://doi.org/10.1007/s10107-017-1180-1.
@article{osti_1371487,
title = {Accelerating the DC algorithm for smooth functions},
author = {Aragón Artacho, Francisco J. and Fleming, Ronan M. T. and Vuong, Phan T.},
abstractNote = {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 Lojasiewicz 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 Lojasiewicz 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.},
doi = {10.1007/s10107-017-1180-1},
journal = {Mathematical Programming},
number = 1,
volume = 169,
place = {Netherlands},
year = {Mon Jul 17 00:00:00 EDT 2017},
month = {Mon Jul 17 00:00:00 EDT 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/s10107-017-1180-1
https://doi.org/10.1007/s10107-017-1180-1
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 37 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
On solving Linear Complementarity Problems by DC programming and DCA
journal, February 2011
- Le Thi, Hoai An; Pham Dinh, Tao
- Computational Optimization and Applications, Vol. 50, Issue 3
Numerical solution for optimization over the efficient set by d.c. optimization algorithms
journal, September 1996
- An, Le Thi Hoai; Tao, Pham Dinh; Muu, Le Dung
- Operations Research Letters, Vol. 19, Issue 3
On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
journal, May 2007
- Attouch, Hedy; Bolte, Jérôme
- Mathematical Programming, Vol. 116, Issue 1-2
Variational Reconstruction with DC-Programming
book, January 2007
- Schnörr, C.; Schüle, T.; Weber, S.
- Advances in Discrete Tomography and Its Applications
Proximal Newton-Type Methods for Minimizing Composite Functions
journal, January 2014
- Lee, Jason D.; Sun, Yuekai; Saunders, Michael A.
- SIAM Journal on Optimization, Vol. 24, Issue 3
Douglas–Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
journal, November 2015
- Li, Guoyin; Pong, Ting Kei
- Mathematical Programming, Vol. 159, Issue 1-2
Convergence of the Iterates of Descent Methods for Analytic Cost Functions
journal, January 2005
- Absil, P. A.; Mahony, R.; Andrews, B.
- SIAM Journal on Optimization, Vol. 16, Issue 2
Trading convexity for scalability
conference, January 2006
- Collobert, Ronan; Sinz, Fabian; Weston, Jason
- Proceedings of the 23rd international conference on Machine learning - ICML '06
A community-driven global reconstruction of human metabolism
journal, March 2013
- Thiele, Ines; Swainston, Neil; Fleming, Ronan M. T.
- Nature Biotechnology, Vol. 31, Issue 5
Detection of stoichiometric inconsistencies in biomolecular models
journal, August 2008
- Gevorgyan, A.; Poolman, M. G.; Fell, D. A.
- Bioinformatics, Vol. 24, Issue 19
Gradient methods for minimizing composite functions
journal, December 2012
- Nesterov, Yu.
- Mathematical Programming, Vol. 140, Issue 1
A generalized proximal point algorithm for certain non-convex minimization problems
journal, January 1981
- Fukushima, Masao; Mine, Hisashi
- International Journal of Systems Science, Vol. 12, Issue 8
A Barzilai–Borwein type method for stochastic linear complementarity problems
journal, November 2013
- Huang, Yakui; Liu, Hongwei; Zhou, Sha
- Numerical Algorithms, Vol. 67, Issue 3
The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
journal, January 2007
- Bolte, Jérôme; Daniilidis, Aris; Lewis, Adrian
- SIAM Journal on Optimization, Vol. 17, Issue 4
A minimization method for the sum of a convex function and a continuously differentiable function
journal, January 1981
- Mine, H.; Fukushima, M.
- Journal of Optimization Theory and Applications, Vol. 33, Issue 1
Globally convergent algorithms for finding zeros of duplomonotone mappings
journal, September 2014
- Aragón Artacho, Francisco J.; Fleming, Ronan M. T.
- Optimization Letters, Vol. 9, Issue 3
A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem
journal, May 1998
- Tao, Pham Dinh; An, Le Thi Hoai
- SIAM Journal on Optimization, Vol. 8, Issue 2