On Solving Nonconvex MINLP Problems with SHOT

  • Andreas LundellEmail author
  • Jan Kronqvist
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


The Supporting Hyperplane Optimization Toolkit (SHOT) solver was originally developed for solving convex MINLP problems, for which it has proven to be very efficient. In this paper, we describe some techniques and strategies implemented in SHOT for improving its performance on nonconvex problems. These include utilizing an objective cut to force an update of the best known solution and strategies for handling infeasibilities resulting from supporting hyperplanes and cutting planes generated from nonconvex constraint functions. For convex problems, SHOT gives a guarantee to find the global optimality, but for general nonconvex problems it will only be a heuristic. However, utilizing some automated transformations it is actually possible in some cases to reformulate all nonconvexities into linear form, ensuring that the obtained solution is globally optimal. Finally, SHOT is compared to other MINLP solvers on a few nontrivial test problems to illustrate its performance.


Nonconvex MINLP Supporting Hyperplane Optimization Toolkit (SHOT) Reformulation techniques Feasibility relaxation 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Science and Engineering, Mathematics and StatisticsÅbo Akademi UniversityTurkuFinland
  2. 2.Department of ComputingImperial College LondonLondonUK

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