A New Warmstarting Strategy for the Primal-Dual Column Generation Method

Technical Report ERGO-12-007

J. Gondzio, P. González-Brevis

This paper presents a new warmstarting technique in the context of a primal-dual column generation method applied to solve a particular class of combinatorial optimization problems. The technique relies on calculating an initial point and on solving auxiliary linear optimization problems to determine the step direction needed to fully restore primal and dual feasibilities after new columns arrive. Conditions on the maximum size of the cuts and on a suitable initial point are discussed. Additionally, the strategy ensures that the duality gap of the warmstart is bounded by the old duality gap multiplied with a (small) constant, which depends on the relation between the old and modified problems. Computational experiments demonstrate the gains achieved when compared to a coldstart approach.

Key words: Interior Point Methods, Warmstarting, Linear Programming, Primal-Dual Methods, Column Generation.

PDF ERGO-12-007.pdf.

Written: June 22, 2012, revised February 1, 2013 and November 8, 2013.
Mathematical Programming A 152 (2015) 113--146.
Published online May 22, 2014.

Related Software:
PDCGM Primal-Dual Column Generation Method.
HOPDM Higher Order Primal Dual Method.