FilMINT: an outer approximation-based solver for convex mixed-integer nonlinear programs. We describe a new solver for convex mixed-integer nonlinear programs (MINLPs) that implements a linearization-based algorithm. The solver is based on an algorithm of {it I. Quesada} and {it I. E. Grossmann} [“An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems.” Comput. Chemical Engrg. 16, No. 10--11, 937--947 (1992)] that avoids the complete re-solution of a master mixed-integer linear program (MILP) by adding new linearizations at open nodes of the branch-and-bound tree whenever an integer solution is found. The new solver, FilMINT, combines the MINTO branch-and-cut framework for MILP with filterSQP to solve the nonlinear programs that arise as subproblems in the algorithm. The MINTO framework allows us to easily employ cutting planes, primal heuristics, and other well-known MILP enhancements for MINLPs. We present detailed computational experiments that show the benefit of such advanced MILP techniques. We offer new suggestions for generating and managing linearizations that are shown to be efficient on a wide range of MINLPs. By carefully incorporating and tuning all these enhancements, an effective solver for convex MINLPs is constructed.

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  1. Frangioni, Antonio; Furini, Fabio; Gentile, Claudio: Approximated perspective relaxations: a project and lift approach (2016)
  2. Jakob Witzig, Timo Berthold, Stefan Heinz: Experiments with Conflict Analysis in Mixed Integer Programming (2016) arXiv
  3. Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma: Polyhedral approximation in mixed-integer convex optimization (2016) arXiv
  4. Trespalacios, Francisco; Grossmann, Ignacio E.: Cutting plane algorithm for convex generalized disjunctive programs (2016)
  5. Gleixner, Ambros M.: Exact and fast algorithms for mixed-integer nonlinear programming (2015)
  6. Hamzeei, Mahdi; Luedtke, James: Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation (2014)
  7. Hijazi, Hassan; Bonami, Pierre; Ouorou, Adam: An outer-inner approximation for separable mixed-integer nonlinear programs (2014)
  8. Kılınç, Mustafa; Linderoth, Jeff; Luedtke, James; Miller, Andrew: Strong-branching inequalities for convex mixed integer nonlinear programs (2014)
  9. Belotti, Pietro: Bound reduction using pairs of linear inequalities (2013)
  10. D’ambrosio, Claudia; Lodi, Andrea: Mixed integer nonlinear programming tools: an updated practical overview (2013)
  11. Fortz, B.; Labbé, M.; Louveaux, F.; Poss, M.: Stochastic binary problems with simple penalties for capacity constraints violations (2013)
  12. Kirches, Christian; Leyffer, Sven: TACO: a toolkit for AMPL control optimization (2013)
  13. Berthold, Timo; Gleixner, Ambros M.; Heinz, Stefan; Vigerske, Stefan: Analyzing the computational impact of MIQCP solver components (2012)
  14. Berthold, Timo; Heinz, Stefan; Vigerske, Stefan: Extending a CIP framework to solve MIQCPs (2012)
  15. Bonami, Pierre; Gonçalves, João P.M.: Heuristics for convex mixed integer nonlinear programs (2012)
  16. Bonami, Pierre; Kilinç, Mustafa; Linderoth, Jeff: Algorithms and software for convex mixed integer nonlinear programs (2012)
  17. Hijazi, Hassan; Bonami, Pierre; Cornuéjols, Gérard; Ouorou, Adam: Mixed-integer nonlinear programs featuring “on/off” constraints (2012)
  18. Ruiz, Juan P.; Grossmann, Ignacio E.: A hierarchy of relaxations for nonlinear convex generalized disjunctive programming (2012)
  19. Sager, Sebastian; Bock, Hans Georg; Diehl, Moritz: The integer approximation error in mixed-integer optimal control (2012)
  20. Toriello, Alejandro; Vielma, Juan Pablo: Fitting piecewise linear continuous functions (2012)

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