Year: 2026
Type: preprint
Abstract: Mixed-integer programs have found applications in many real-world problems but remain difficult to solve at scale. To improve scalability, there has been increasing interest in incorporating first-order methods as subroutines for solving node relaxations, with success primarily on problems involving specific types of constraints. However, when more general constraints are considered, first-order methods cannot be directly applied because, at finite iterations, they typically produce infeasible primal and dual solutions, preventing their direct integration into branch-and-bound. To overcome this limitation, we introduce repair procedures that extract valid primal and dual bounds from infeasible first-order iterates. These bounds enable node pruning, incumbent updates, and early stopping at any iteration. Empirically, our approach achieves one to two orders of magnitude speedups when solving real-world instances (with another order of magnitude speedup when running on GPUs) and certifies optimality on instances that are difficult for commercial solvers.
Source: arXiv (Cornell University)
Authors: Pivi, Francesco, Liu, Jiachang, Lodi, Andrea
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1267976811, G1453181110, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G2554637905, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, G5897173182, G7113600513, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W7223066429