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

References in zbMATH (referenced in 28 articles , 1 standard article )

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  1. Lundell, Andreas; Kronqvist, Jan: Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT (2022)
  2. Sharma, Meenarli; Palkar, Prashant; Mahajan, Ashutosh: Linearization and parallelization schemes for convex mixed-integer nonlinear optimization (2022)
  3. Vogt, Ryan H.; Leyffer, Sven; Munson, Todd S.: A mixed-integer PDE-constrained optimization formulation for electromagnetic cloaking (2022)
  4. Atamturk, Alper; Gomez, Andres; Han, Shaoning: Sparse and smooth signal estimation: convexification of (\ell_0)-formulations (2021)
  5. Berthold, Timo; Witzig, Jakob: Conflict analysis for MINLP (2021)
  6. Gómez, Andrés: Strong formulations for conic quadratic optimization with indicator variables (2021)
  7. Gómez, Andrés; Prokopyev, Oleg A.: A mixed-integer fractional optimization approach to best subset selection (2021)
  8. Kronqvist, Jan; Misener, Ruth: A disjunctive cut strengthening technique for convex MINLP (2021)
  9. Mahajan, Ashutosh; Leyffer, Sven; Linderoth, Jeff; Luedtke, James; Munson, Todd: Minotaur: a mixed-integer nonlinear optimization toolkit (2021)
  10. Sharma, Meenarli; Hahn, Mirko; Leyffer, Sven; Ruthotto, Lars; van Bloemen Waanders, Bart: Inversion of convection-diffusion equation with discrete sources (2021)
  11. Ceccon, Francesco; Siirola, John D.; Misener, Ruth: SUSPECT: MINLP special structure detector for Pyomo (2020)
  12. D’Ambrosio, Claudia; Frangioni, Antonio; Gentile, Claudio: Strengthening the sequential convex MINLP technique by perspective reformulations (2019)
  13. Atamtürk, Alper; Gómez, Andrés: Strong formulations for quadratic optimization with M-matrices and indicator variables (2018)
  14. Kröger, Ole; Coffrin, Carleton; Hijazi, Hassan; Nagarajan, Harsha: Juniper: an open-source nonlinear branch-and-bound solver in Julia (2018)
  15. Lubin, Miles; Yamangil, Emre; Bent, Russell; Vielma, Juan Pablo: Polyhedral approximation in mixed-integer convex optimization (2018)
  16. Mustonen, Lauri; Gao, Xiangxi; Santana, Asteroide; Mitchell, Rebecca; Vigfusson, Ymir; Ruthotto, Lars: A Bayesian framework for molecular strain identification from mixed diagnostic samples (2018)
  17. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F. Javier: An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution (2016)
  18. Alonso-Ayuso, Antonio; Escudero, Laureano F.; Martín-Campo, F. Javier: Multiobjective optimization for aircraft conflict resolution. A metaheuristic approach (2016)
  19. Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma: Polyhedral approximation in mixed-integer convex optimization (2016) arXiv
  20. 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)

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