Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Numerical Experience with Lower Bounds for MIQP Branch-And-Bound
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
IEEE Transactions on Signal Processing
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Proceedings of the 2nd ACM international conference on High confidence networked systems
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The main objective in this work is to compare different convex relaxations for Model Predictive Control (MPC) problems with mixed real valued and binary valued control signals. In the problem description considered, the objective function is quadratic, the dynamics are linear, and the inequality constraints on states and control signals are all linear. The relaxations are related theoretically and the quality of the bounds and the computational complexities are compared in numerical experiments. The investigated relaxations include the Quadratic Programming (QP) relaxation, the standard Semidefinite Programming (SDP) relaxation, and an equality constrained SDP relaxation. The equality constrained SDP relaxation appears to be new in the context of hybrid MPC and the result presented in this work indicates that it can be useful as an alternative relaxation, which is less computationally demanding than the ordinary SDP relaxation and which often gives a better bound than the bound from the QP relaxation. Furthermore, it is discussed how the result from the SDP relaxations can be used to generate suboptimal solutions to the control problem. Moreover, it is also shown that the equality constrained SDP relaxation is equivalent to a QP in an important special case.