Abstract
We present a version of the Frank-Wolfe method for linearly const rained convex programs, in which consecutive search direction are made conjugate to each other. We also present preliminary computat ional studies in a MATLAB environment. In these we apply the pure Frank-Wolfe, the Conjugate Direction Frank-Wolfe(CDFW) and the “partanized” Frank-Wolfe to some classical Traffic Assignment Problems. CDFW compares favorably to the other methods in this study
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arezki, Y. and van Vliet, D. (1990) A full analytical implementation of the PARTAN/Frank-Wolfe algorithm for equilibrium assignment. Transportation Sci.24 (1), 58–62.
Bruynooghe, M., Gibert, A. and Sakarovitch, M. (1969) Une mé thode d'affectation du trafic. Proceedings of the 4th International Symposium on the Theory of Road Traffic Flow, Bundesminister für Verkehr, Bonn, 198–204.
Florian, M., Guelat, J. and Spiess, H. (1987) An efficient implementation of the “PARTAN” variant of the linear approximation method for the network equilibrium problem. Networks 17, 319–339.
Frank, M. and Wolfe, P. (1956) An algorithm for quadratic programming. Naval Res. Logist. Quart. 3, 95–110.
Fratta, L., GerIa, M. and Kleinrock, L. (1973) Th e flow deviat ion method:An approach to st ore-and-forward communicat ion network design. Networks 3,97–133.
Fukushima, M. (1984) A modified Frank-Wolfe algorithm for solving th e traffic assignment problem. Transportation Res. Part B 18 (2), 169–177
Larsson, T., Patriksson, M. and Rydergren, C. (1997) Applicat ions of simplicial decomposition with nonlinear column generation to nonlinear network flows.Network opt imization, 346–373. Springer, Berlin.
LeBlanc, L. J. (1973) Mat hematical programmin g algorit hms for large scale network equilibrium and network design problems. PhD thesis, IE/MS Dept,Northwestern University, Evansto n IL.
LeBlan c, L., Helgason, R. and Boyce, D. (1985) Improved efficiency of the Fra nk-Wolfe algorithm for convex network programs. Transportation Sci. 19 (4),.445–462
Luenberger,D.G. (1984) Linear and Nonlinear Programming. Addison-Wesley,Reading, MA.
Lupi, M. (1986) Convergence of the Frank-Wolfe algorithm in transportation network. Civil Engineering Systems 3, 7–15
Matlab Reference Guide (1996), The MathWorks, Mass.
Ouorou, A., Mahey, P. and Vial, J.P. (2000) A survey of algorit hms for convex mult icommodity flow problems. Management Sci. 46 (1), 126–147.
Patriksson, M. (1994) The Traffic Assignment Problem - Models and Methods.VSP, Utrecht, The Netherlands.
Powell, W. and Sheffi, Y. (1982) The convergence of equilibrium algorit hms with predetermined step sizes. Transportation Sci. 16 (1), 45–55.
Shah, B., Buehler, R. and Kempth orne, O. (1964) Some algorithms for minimizing a function of several variables. J. Soc. Indust. Appl, Mat h. 12, 74–92
Weint raub, A., Ortiz, C. and Gonzá lez, J. (1985) Accelerating convergence of t he Fr ank-Wolfe algorithm. Transportat ion Res. Part B 19 (2), 113–122
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Daneva, M., Lindberg, P.O. (2003). A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem. In: Leopold-Wildburger, U., Rendl, F., Wäscher, G. (eds) Operations Research Proceedings 2002. Operations Research Proceedings 2002, vol 2002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55537-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-55537-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00387-8
Online ISBN: 978-3-642-55537-4
eBook Packages: Springer Book Archive