Large-scale optimization with the primal-dual column generation method

The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant allows to obtain suboptimal and well-centered dual solutions which naturally stabilizes the column generation. A reduction in the number of calls … Read more

A new warmstarting strategy for the primal-dual column generation method

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 … Read more

New developments in the primal-dual column generation technique

The classical column generation is based on optimal solutions of the restricted master problems. This strategy frequently results in an unstable behaviour and may require an unnecessarily large number of iterations. To overcome this weakness, variations of the classical approach use interior points of the dual feasible set, instead of optimal solutions. In this paper, … Read more