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. Lodi, Andrea; Malaguti, Enrico; Nannicini, Giacomo; Thomopulos, Dimitri: Nonlinear chance-constrained problems with applications to hydro scheduling (2022)
  2. Sharma, Meenarli; Palkar, Prashant; Mahajan, Ashutosh: Linearization and parallelization schemes for convex mixed-integer nonlinear optimization (2022)
  3. Gómez, Andrés; Prokopyev, Oleg A.: A mixed-integer fractional optimization approach to best subset selection (2021)
  4. Kleinert, Thomas; Grimm, Veronika; Schmidt, Martin: Outer approximation for global optimization of mixed-integer quadratic bilevel problems (2021)
  5. Mahajan, Ashutosh; Leyffer, Sven; Linderoth, Jeff; Luedtke, James; Munson, Todd: Minotaur: a mixed-integer nonlinear optimization toolkit (2021)
  6. Sharma, Meenarli; Hahn, Mirko; Leyffer, Sven; Ruthotto, Lars; van Bloemen Waanders, Bart: Inversion of convection-diffusion equation with discrete sources (2021)
  7. Leyffer, Sven; Vanaret, Charlie: An augmented Lagrangian filter method (2020)
  8. Lubin, Miles; Yamangil, Emre; Bent, Russell; Vielma, Juan Pablo: Polyhedral approximation in mixed-integer convex optimization (2018)
  9. Lu, Jie; Gupte, Akshay; Huang, Yongxi: A mean-risk mixed integer nonlinear program for transportation network protection (2018)
  10. Reid, Stephen; Newman, Aaron M.; Diehn, Maximilian; Alizadeh, Ash A.; Tibshirani, Robert: Genomic feature selection by coverage design optimization (2018)
  11. Kılınç, Mustafa R.; Linderoth, Jeff; Luedtke, James: Lift-and-project cuts for convex mixed integer nonlinear programs (2017)
  12. Vielma, Juan Pablo; Dunning, Iain; Huchette, Joey; Lubin, Miles: Extended formulations in mixed integer conic quadratic programming (2017)
  13. Vinel, Alexander; Krokhmal, Pavlo A.: Mixed integer programming with a class of nonlinear convex constraints (2017)
  14. Frangioni, Antonio; Furini, Fabio; Gentile, Claudio: Approximated perspective relaxations: a project and lift approach (2016)
  15. Jakob Witzig, Timo Berthold, Stefan Heinz: Experiments with Conflict Analysis in Mixed Integer Programming (2016) arXiv
  16. Lubin, Miles; Yamangil, Emre; Bent, Russell; Vielma, Juan Pablo: Extended formulations in mixed-integer convex programming (2016)
  17. Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma: Polyhedral approximation in mixed-integer convex optimization (2016) arXiv
  18. Trespalacios, Francisco; Grossmann, Ignacio E.: Cutting plane algorithm for convex generalized disjunctive programs (2016)
  19. Gleixner, Ambros M.: Exact and fast algorithms for mixed-integer nonlinear programming (2015)
  20. Hamzeei, Mahdi; Luedtke, James: Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation (2014)

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