A Proximal Trust-Region Algorithm for Column Generation Stabilization

This paper proposes a generalization of the proximal point algorithm using both penalty and trust region concepts. Finite convergence is established while assuming the trust regions are of full dimension and never shrink to a single point. The approach is specialized to the cutting plane/column generation context. The resulting algorithm ensures convergence to a pair of primal and dual optimal solutions. Computational experiments carried over multi-depot vehicle scheduling instances show a great stabilizing and accelerating effect on column generation method.