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A Unified Early Termination Technique for Primal-dual Algorithms in Mixed Integer Conic Programming

Yuwen ChenCatherine NingPaul Goulart
Mar 2023
We propose an early termination technique for mixed integer conic programmingfor use within branch-and-bound based solvers. Our approach generalizesprevious early termination results for ADMM-based solvers to a broader class ofprimal-dual algorithms, including both operator splitting methods and interiorpoint methods. The complexity for checking early termination is $O(n)$ for eachtermination check assuming a bounded problem domain. We show that this domainrestriction can be relaxed for problems whose data satisfies a simple rankcondition, in which case each check requires an $O(n^2)$ solve using a linearsystem that must be factored only once at the root node. We further show howthis approach can be used in hybrid model predictive control as long as systeminputs are bounded. Numerical results show that our method leads to a moderatereduction in the total iterations required for branch-and-bound conic solverswith interior-point based subsolvers.