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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  1. Fernández, F.J.; Alvarez-Vázquez, L.J.; Martínez, A.; Vázquez-Méndez, M.E.: A 3D optimal control problem related to the urban heat islands (2017)
  2. Mencarelli, Luca; Sahraoui, Youcef; Liberti, Leo: A multiplicative weights update algorithm for MINLP (2017)
  3. Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks (2017)
  4. Belotti, Pietro; Bonami, Pierre; Fischetti, Matteo; Lodi, Andrea; Monaci, Michele; Nogales-Gómez, Amaya; Salvagnin, Domenico: On handling indicator constraints in mixed integer programming (2016)
  5. Borraz-Sánchez, Conrado; Bent, Russell; Backhaus, Scott; Hijazi, Hassan; Van Hentenryck, Pascal: Convex relaxations for gas expansion planning (2016)
  6. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  7. Buchheim, Christoph; De Santis, Marianna; Lucidi, Stefano; Rinaldi, Francesco; Trieu, Long: A feasible active set method with reoptimization for convex quadratic mixed-integer programming (2016)
  8. Fampa, Marcia; Lee, Jon; Melo, Wendel: A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in $n$-space (2016)
  9. Gassmann, Horand; Ma, Jun; Martin, Kipp: Communication protocols for options and results in a distributed optimization environment (2016)
  10. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  11. Kılınç-Karzan, Fatma: On minimal valid inequalities for mixed integer conic programs (2016)
  12. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming (2016)
  13. Sharma, Shaurya; Knudsen, Brage Rugstad; Grimstad, Bjarne: Towards an objective feasibility pump for convex minlps (2016)
  14. Boland, N.L.; Eberhard, A.C.: On the augmented Lagrangian dual for integer programming (2015)
  15. D’Ambrosio, Claudia; Lodi, Andrea; Wiese, Sven; Bragalli, Cristiana: Mathematical programming techniques in water network optimization (2015)
  16. Fernández, F.J.; Alvarez-Vázquez, L.J.; García-Chan, N.; Martínez, A.; Vázquez-Méndez, M.E.: Optimal location of green zones in metropolitan areas to control the urban heat island (2015)
  17. Ghaddar, Bissan; Naoum-Sawaya, Joe; Kishimoto, Akihiro; Taheri, Nicole; Eck, Bradley: A Lagrangian decomposition approach for the pump scheduling problem in water networks (2015)
  18. Hiller, Benjamin; Humpola, Jesco; Lehmann, Thomas; Lenz, Ralf; Morsi, Antonio; Pfetsch, Marc E.; Schewe, Lars; Schmidt, Martin; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Willert, Bernhard M.: Computational results for validation of nominations (2015)
  19. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  20. Kirst, Peter; Stein, Oliver; Steuermann, Paul: Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints (2015)

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