Bonmin

An algorithmic framework for convex mixed integer nonlinear programs. This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available.


References in zbMATH (referenced in 211 articles )

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  2. Dam, Tien Thanh; Ta, Thuy Anh; Mai, Tien: Submodularity and local search approaches for maximum capture problems under generalized extreme value models (2022)
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  5. Lundell, Andreas; Kronqvist, Jan: Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT (2022)
  6. Paat, Joseph; Schlöter, Miriam; Speakman, Emily: Constructing lattice-free gradient polyhedra in dimension two (2022)
  7. Sharma, Meenarli; Palkar, Prashant; Mahajan, Ashutosh: Linearization and parallelization schemes for convex mixed-integer nonlinear optimization (2022)
  8. Vogt, Ryan H.; Leyffer, Sven; Munson, Todd S.: A mixed-integer PDE-constrained optimization formulation for electromagnetic cloaking (2022)
  9. Berthold, Timo; Witzig, Jakob: Conflict analysis for MINLP (2021)
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  11. Bonvin, Gratien; Demassey, Sophie; Lodi, Andrea: Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound (2021)
  12. Brito, Samuel Souza; Santos, Haroldo Gambini: Preprocessing and cutting planes with conflict graphs (2021)
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  14. Gómez, Andrés; Prokopyev, Oleg A.: A mixed-integer fractional optimization approach to best subset selection (2021)
  15. Kleinert, Thomas; Grimm, Veronika; Schmidt, Martin: Outer approximation for global optimization of mixed-integer quadratic bilevel problems (2021)
  16. Kronqvist, Jan; Misener, Ruth: A disjunctive cut strengthening technique for convex MINLP (2021)
  17. Larson, Jeffrey; Leyffer, Sven; Palkar, Prashant; Wild, Stefan M.: A method for convex black-box integer global optimization (2021)
  18. Liu, Yanchao: A note on solving DiDi’s driver-order matching problem (2021)
  19. Murray, Alexander; Faulwasser, Timm; Hagenmeyer, Veit; Villanueva, Mario E.; Houska, Boris: Partially distributed outer approximation (2021)
  20. Neumann, Christoph; Stein, Oliver: Generating feasible points for mixed-integer convex optimization problems by inner parallel cuts (2021)

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