Jan Kronqvist

Separating Hyperplanes for Mixed-Integer Polynomial Optimization Problems

  • Carl Eggen
  • Jan Kronqvist
  • Andreas Lundell
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Semi-definite Programming Tags , , ,

    Algorithms based on polyhedral outer approximations provide a powerful approach to solving mixed-integer nonlinear optimization problems. An initial relaxation of the feasible set is strengthened by iteratively adding linear inequalities and separating infeasible points. However, when the constraints are nonconvex, computing such separating hyperplanes becomes challenging. In this article, the moment-/sums-of-squares hierarchy is used in … Read more

    Alternative Regularizations for OA Algorithms for Convex MINLP

  • David E. Bernal Neira
  • Ignacio E. Grossmann
  • Jan Kronqvist
  • Zedong Peng
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Nonsmooth Optimization

    In this work, we extend the regularization framework from Kronqvist et al. (https://doi.org/10.1007/s10107-018-1356-3) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance-metrics and Lagrangean approximations, used in the projection problem for finding new … Read more

    A disjunctive cut strengthening technique for convex MINLP

  • Jan Kronqvist
  • Ruth Misener
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    Generating polyhedral outer approximations and solving mixed-integer linear relaxations remains one of the main approaches for solving convex mixed-integer nonlinear programming (MINLP) problems. There are several algorithms based on this concept, and the efficiency is greatly affected by the tightness of the outer approximation. In this paper, we present a new framework for strengthening cutting … Read more

    Polyhedral Approximation Strategies in Nonconvex Mixed-Integer Nonlinear Programming

  • Jan Kronqvist
  • Andreas Lundell
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software Benchmark, Optimization Software Design Principles

    Different versions of polyhedral outer approximation is used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well for convex MINLP, extending them to solve also nonconvex problems has been challenging. One solver based on outer linearization of the nonlinear feasible set of MINLP problems is the … Read more

    The Supporting Hyperplane Optimization Toolkit

  • Jan Kronqvist
  • Andreas Lundell
  • Tapio Westerlund
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems Tags , , , , ,

    In this paper, an open source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The outer approximation is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended … Read more