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. Atamturk, Alper; Gomez, Andres; Han, Shaoning: Sparse and smooth signal estimation: convexification of (\ell_0)-formulations (2021)
  2. Berthold, Timo; Witzig, Jakob: Conflict analysis for MINLP (2021)
  3. Gómez, Andrés: Strong formulations for conic quadratic optimization with indicator variables (2021)
  4. Gómez, Andrés; Prokopyev, Oleg A.: A mixed-integer fractional optimization approach to best subset selection (2021)
  5. Ceccon, Francesco; Siirola, John D.; Misener, Ruth: SUSPECT: MINLP special structure detector for Pyomo (2020)
  6. D’Ambrosio, Claudia; Frangioni, Antonio; Gentile, Claudio: Strengthening the sequential convex MINLP technique by perspective reformulations (2019)
  7. Atamtürk, Alper; Gómez, Andrés: Strong formulations for quadratic optimization with M-matrices and indicator variables (2018)
  8. Kröger, Ole; Coffrin, Carleton; Hijazi, Hassan; Nagarajan, Harsha: Juniper: an open-source nonlinear branch-and-bound solver in Julia (2018)
  9. Lubin, Miles; Yamangil, Emre; Bent, Russell; Vielma, Juan Pablo: Polyhedral approximation in mixed-integer convex optimization (2018)
  10. Mustonen, Lauri; Gao, Xiangxi; Santana, Asteroide; Mitchell, Rebecca; Vigfusson, Ymir; Ruthotto, Lars: A Bayesian framework for molecular strain identification from mixed diagnostic samples (2018)
  11. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F. Javier: An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution (2016)
  12. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F. Javier: Multiobjective optimization for aircraft conflict resolution. A metaheuristic approach (2016)
  13. Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma: Polyhedral approximation in mixed-integer convex optimization (2016) arXiv
  14. 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)
  15. Gleixner, Ambros M.: Exact and fast algorithms for mixed-integer nonlinear programming (2015)
  16. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  17. Valle, C. A.; Meade, N.; Beasley, J. E.: An optimisation approach to constructing an exchange-traded fund (2015)
  18. Berthold, Timo; Gleixner, Ambros M.: Undercover: a primal MINLP heuristic exploring a largest sub-MIP (2014)
  19. Hamzeei, Mahdi; Luedtke, James: Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation (2014)
  20. López, C. O.; Beasley, J. E.: A note on solving MINLP’s using formulation space search (2014)

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