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. De Santis, Marianna; Grani, Giorgio; Palagi, Laura: Branching with hyperplanes in the criterion space: the frontier partitioner algorithm for biobjective integer programming (2020)
  2. Löschenbrand, Markus: Finding multiple Nash equilibria via machine learning-supported Gröbner bases (2020)
  3. Andrade, Tiago; Oliveira, Fabricio; Hamacher, Silvio; Eberhard, Andrew: Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming (2019)
  4. Elloumi, Sourour; Lambert, Amélie: Global solution of non-convex quadratically constrained quadratic programs (2019)
  5. Gronski, Jessica; Ben Sassi, Mohamed-Amin; Becker, Stephen; Sankaranarayanan, Sriram: Template polyhedra and bilinear optimization (2019)
  6. Pankratov, A.; Romanova, T.; Litvinchev, I.: Packing ellipses in an optimized convex polygon (2019)
  7. Schmidt, Martin; Sirvent, Mathias; Wollner, Winnifried: A decomposition method for MINLPs with Lipschitz continuous nonlinearities (2019)
  8. Zamani, Moslem: A new algorithm for concave quadratic programming (2019)
  9. Hartillo, M. I.; Jiménez-Cobano, J. M.; Ucha, J. M.: Finding multiple solutions in nonlinear integer programming with algebraic test-sets (2018)
  10. Jiménez Cobano, José Manuel; Ucha Enríquez, José María: Finding multiplies solutions for non-linear integer programming (2018)
  11. Montanher, Tiago; Neumaier, Arnold; Domes, Ferenc: A computational study of global optimization solvers on two trust region subproblems (2018)
  12. Schweiger, Jonas: Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty (2018)
  13. Belotti, Pietro; Berthold, Timo: Three ideas for a feasibility pump for nonconvex MINLP (2017)
  14. Billionnet, Alain; Elloumi, Sourour; Lambert, Amélie; Wiegele, Angelika: Using a conic bundle method to accelerate both phases of a quadratic convex reformulation (2017)
  15. Fampa, Marcia; Lee, Jon; Melo, Wendel: On global optimization with indefinite quadratics (2017)
  16. Ghaddar, Bissan; Claeys, Mathieu; Mevissen, Martin; Eck, Bradley J.: Polynomial optimization for water networks: global solutions for the valve setting problem (2017)
  17. Gleixner, Ambros M.; Berthold, Timo; Müller, Benjamin; Weltge, Stefan: Three enhancements for optimization-based bound tightening (2017)
  18. Hart, William E.; Laird, Carl D.; Watson, Jean-Paul; Woodruff, David L.; Hackebeil, Gabriel A.; Nicholson, Bethany L.; Siirola, John D.: Pyomo -- optimization modeling in Python (2017)
  19. Hijazi, Hassan; Coffrin, Carleton; Van Hentenryck, Pascal: Convex quadratic relaxations for mixed-integer nonlinear programs in power systems (2017)
  20. Khan, Kamil A.; Watson, Harry A. J.; Barton, Paul I.: Differentiable McCormick relaxations (2017)

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