Mix-CALADIN: A Distributed Algorithm for Consensus Mixed-Integer Optimization
For distributed optimization problems with mixed-integer variables, this work provides a novel algorithm with convergence guarantees, though the improvement over existing methods is incremental.
This paper introduces a distributed algorithm for consensus mixed-integer optimization, extending CALADIN to handle Boolean variables without local mixed-integer solvers. The algorithm achieves competitive performance with rigorous convergence guarantees for convex and nonconvex problems.
This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian Alternating Direction Inexact Newton (CALADIN) framework by incorporating specialized techniques for handling Boolean variables without relying on local mixed-integer solvers. Under the mild assumption of Lipschitz continuity of the objective functions, we establish rigorous convergence guarantees for both convex and nonconvex mixed-integer programming problems. Numerical experiments demonstrate that the proposed algorithm achieves competitive performance compared to existing approaches while providing rigorous convergence guarantees.