, Volume 87, Issue 3, pp 385-399

The volume algorithm: producing primal solutions with a subgradient method

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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.

Received: June 15, 1998 / Accepted: November 15, 1999¶Published online March 15, 2000