Mathematical Programming

, Volume 87, Issue 3, pp 385-399

First online:

The volume algorithm: producing primal solutions with a subgradient method

  • Francisco BarahonaAffiliated withIBM T.J. Watson Research Center, Yorktown Heights, NY 10598
  • , Ranga AnbilAffiliated withIBM T.J. Watson Research Center, Yorktown Heights, NY 10598

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Abstract.

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