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We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal discretizations as well as mixed-integer states and controls (e.g., scheduling logic and discrete actuators). The approach uses a nested cutting-plane scheme that performs forward and backward sweeps along the time horizon to adaptively approximate cost-to-go functions. The DDIP scheme proposed can handle general MPC formulations with mixed-integer controls and states and can perform forward-backward sweeps over block time partitions. We demonstrate the performance of the proposed scheme by solving mixed-integer MPC problems that arise in the scheduling of central heating, ventilation, and air-conditioning (HVAC) plants. We show that the proposed scheme is scalable and dramatically outperforms state-of-the-art mixed-integer solvers.
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are amenable to ex
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden witho
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a sub
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, rel
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing resources, this