Bregman Proximal Relaxation of Large-Scale 0–1 Problems

We apply a recent extension of the Bregman proximal method for convex programming to LP relaxations of 0–1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.

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