We propose a new inexact column-and-constraint generation (i-C&CG) method to solve two-stage robust optimization problems. The method allows solutions to the master problems to be inexact, which is desirable when solving large-scale and/or challenging problems. It is equipped with a backtracking routine that controls the trade-off between bound improvement and inexactness. Importantly, this routine allows us to derive theoretical finite convergence guarantees for our i-C&CG method. Numerical experiments demonstrate computational advantages of our i-C&CG method over state-of-the-art column-and-constraint generation methods.
@article{arxiv.2207.03291,
title = {An inexact column-and-constraint generation method to solve two-stage robust optimization problems},
author = {Man Yiu Tsang and Karmel S. Shehadeh and Frank E. Curtis},
journal= {arXiv preprint arXiv:2207.03291},
year = {2022}
}