supporting hyperplane optimization toolkit (shot)

Decomposition-Based Reformulation of Nonseparable Quadratic Expressions in Convex MINLP

  • Joakim Blomqvist
  • etamm
  • Jan Kronqvist
  • Andreas Lundell
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization, Global Optimization Tags , , , , , ,

    In this paper, we present a reformulation technique for convex mixed-integer nonlinear programming (MINLP) problems with nonseparable quadratic terms. For each convex non-diagonal matrix that defines quadratic expressions in the problem, we show that an eigenvalue or LDLT decomposition can be performed to transform the quadratic expressions into convex additively separable constraints. The reformulated problem … 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