MINOTAUR is a toolkit for solving mixed-integer nonlinear optimization problems. We study methods for building polyhedral relaxations of multilinear terms that arise in nonconvex mixed integer optimization problems. The goal is to obtain a formulation that is more compact than the convex hull formulation, but yields tighter relaxations than the standard McCormick relaxation. We present computational results for an approach based on grouping the variables into subsets that cover all multilinear terms in the problem. The approach is combined with additional reformulation techniques and spatial branching in the software framework MINOTAUR to produce a solver for mixed integer polynomial optimization problems

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  1. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F.Javier: Multiobjective optimization for aircraft conflict resolution. A metaheuristic approach (2016)
  2. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F. Javier: An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution (2016)
  3. Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma: Polyhedral approximation in mixed-integer convex optimization (2016) arXiv
  4. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F.Javier; Mladenović, Nenad: A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes (2015)
  5. Gleixner, Ambros M.: Exact and fast algorithms for mixed-integer nonlinear programming (2015)
  6. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  7. Valle, C.A.; Meade, N.; Beasley, J.E.: An optimisation approach to constructing an exchange-traded fund (2015)
  8. Berthold, Timo; Gleixner, Ambros M.: Undercover: a primal MINLP heuristic exploring a largest sub-MIP (2014)
  9. Hamzeei, Mahdi; Luedtke, James: Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation (2014)
  10. López, C.O.; Beasley, J.E.: A note on solving MINLP’s using formulation space search (2014)
  11. Pruitt, Kristopher A.; Leyffer, Sven; Newman, Alexandra M.; Braun, Robert J.: A mixed-integer nonlinear program for the optimal design and dispatch of distributed generation systems (2014)
  12. Valle, C.A.; Meade, N.; Beasley, J.E.: Market neutral portfolios (2014)