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.

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  10. Kirches, C.; Lenders, F.; Manns, P.: Approximation properties and tight bounds for constrained mixed-integer optimal control (2020)
  11. Kronqvist, Jan; Bernal, David E.; Grossmann, Ignacio E.: Using regularization and second order information in outer approximation for convex MINLP (2020)
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  13. Mai, Tien; Lodi, Andrea: A multicut outer-approximation approach for competitive facility location under random utilities (2020)
  14. Melo, Wendel; Fampa, Marcia; Raupp, Fernanda: An overview of MINLP algorithms and their implementation in Muriqui optimizer (2020)
  15. Neumann, Christoph; Stein, Oliver; Sudermann-Merx, Nathan: Granularity in nonlinear mixed-integer optimization (2020)
  16. Torkaman, Somayeh; Akbari Jokar, Mohammad Reza; Mutlu, Nevin; Van Woensel, Tom: Solving a production-routing problem with price-dependent demand using an outer approximation method (2020)
  17. Andersson, Joel A. E.; Gillis, Joris; Horn, Greg; Rawlings, James B.; Diehl, Moritz: CasADi: a software framework for nonlinear optimization and optimal control (2019)
  18. Bei, Xiaoqiang; Zhu, Xiaoyan; Coit, David W.: A risk-averse stochastic program for integrated system design and preventive maintenance planning (2019)
  19. Bellahcene, Fatima: Application of the polyblock method to special integer chance constrained problem (2019)
  20. Benítez-Peña, Sandra; Blanquero, Rafael; Carrizosa, Emilio; Ramírez-Cobo, Pepa: On support vector machines under a multiple-cost scenario (2019)

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