@article{eprints3642,
          number = {23},
           pages = {73--79},
          volume = {48},
            year = {2015},
           title = {Solving Mixed-Integer Quadratic Programs via Nonnegative Least Squares},
          author = {Alberto Bemporad},
         journal = {IFAC-PapersOnLine},
       publisher = {Elsevier},
            note = {5th IFAC Conference on Nonlinear Model Predictive Control NMPC 2015 - Seville, Spain, 17?20 September 2015},
             url = {http://eprints.imtlucca.it/3642/},
        abstract = {This paper proposes a new algorithm for solving Mixed-Integer Quadratic Programming (MIQP) problems. The algorithm is particularly tailored to solving small-scale MIQPs such as those that arise in embedded hybrid Model Predictive Control (MPC) applications. The approach combines branch and bound (B\&B) with nonnegative least squares (NNLS), that are used to solve Quadratic Programming (QP) relaxations. The QP algorithm extends a method recently proposed by the author for solving strictly convex QP's, by (i) handling equality and bilateral inequality constraints, (ii) warm starting, and (iii) exploiting easy-to-compute lower bounds on the optimal cost to reduce the number of QP iterations required to solve the relaxed problems. The proposed MIQP algorithm has a speed of execution that is comparable to state- of-the-art commercial MIQP solvers and is relatively simple to code, as it requires only basic arithmetic operations to solve least-square problems.}
}