Mathematical Programming

, Volume 87, Issue 3, pp 385–399

The volume algorithm: producing primal solutions with a subgradient method

  • Francisco Barahona
  • Ranga Anbil

DOI: 10.1007/s101070050002

Cite this article as:
Barahona, F. & Anbil, R. Math. Program. (2000) 87: 385. doi:10.1007/s101070050002


We present an extension to the subgradient algorithm to produce primal as well as dual solutions. It can be seen as a fast way to carry out an approximation of Dantzig-Wolfe decomposition. This gives a fast method for producing approximations for large scale linear programs. It is based on a new theorem in linear programming duality. We present successful experience with linear programs coming from set partitioning, set covering, max-cut and plant location.

Key words: subgradient algorithm – Dantzig-Wolfe decomposition – large scale linear programming
Mathematics Subject Classification (1991): 90C05, 90C06

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Francisco Barahona
    • 1
  • Ranga Anbil
    • 1
  1. 1.IBM T.J. Watson Research Center, Yorktown Heights, NY 10598US