Branching and bounds tightening techniques for non-connvex MINLP. Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial Branch& Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for real-world MINLP problems, we have developed an sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) and used it for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver.

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  1. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  2. Dalkiran, Evrim; Sherali, Hanif D.: RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems (2016)
  3. Gassmann, Horand; Ma, Jun; Martin, Kipp: Communication protocols for options and results in a distributed optimization environment (2016)
  4. Lejeune, Miguel A.; Margot, François: Solving chance-constrained optimization problems with stochastic quadratic inequalities (2016)
  5. Bao, Xiaowei; Khajavirad, Aida; Sahinidis, Nikolaos V.; Tawarmalani, Mohit: Global optimization of nonconvex problems with multilinear intermediates (2015)
  6. Gago-Vargas, J.; Hartillo, I.; Puerto, J.; Ucha, J.M.: An improved test set approach to nonlinear integer problems with applications to engineering design (2015)
  7. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  8. Araya, Ignacio; Trombettoni, Gilles; Neveu, Bertrand; Chabert, Gilles: Upper bounding in inner regions for global optimization under inequality constraints (2014)
  9. Carrizosa, Emilio; Guerrero, Vanesa: $rs$-sparse principal component analysis: a mixed integer nonlinear programming approach with VNS (2014)
  10. Kogan, Alexander; Lejeune, Miguel A.: Threshold Boolean form for joint probabilistic constraints with random technology matrix (2014)
  11. Le Thi, Hoai An; Tran, Duc Quynh: Optimizing a multi-stage production/inventory system by DC programming based approaches (2014)
  12. Patil, Bhagyesh V.; Nataraj, P.S.V.: An improved Bernstein global optimization algorithm for MINLP problems with application in process industry (2014)
  13. Pruitt, Kristopher A.; Leyffer, Sven; Newman, Alexandra M.; Braun, Robert J.: A mixed-integer nonlinear program for the optimal design and dispatch of distributed generation systems (2014)
  14. Zorn, Keith; Sahinidis, Nikolaos V.: Global optimization of general nonconvex problems with intermediate polynomial substructures (2014)
  15. Zorn, Keith; Sahinidis, Nikolaos V.: Global optimization of general non-convex problems with intermediate bilinear substructures (2014)
  16. Belotti, Pietro: Bound reduction using pairs of linear inequalities (2013)
  17. Buchheim, C.; De Santis, M.; Palagi, L.; Piacentini, M.: An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations (2013)
  18. Buchheim, Christoph; Wiegele, Angelika: Semidefinite relaxations for non-convex quadratic mixed-integer programming (2013)
  19. Cassioli, A.; Consolini, L.; Locatelli, M.; Longo, A.: Optimization and homotopy methods for the Gibbs free energy of simple magmatic mixtures (2013)
  20. Gentilini, Iacopo; Margot, François; Shimada, Kenji: The travelling salesman problem with neighbourhoods: MINLP solution (2013)

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