Carl Eggen

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

    Granularity for mixed-integer polynomial optimization problems

  • Carl Eggen
  • Oliver Stein
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , , ,

    Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sos-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sos-hierarchy is hereby used to solve those … Read more

    Considering homeowner acceptance of retrofit measures within energy supply network optimization

  • Carl Eggen
  • Moritz Link
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , ,

    A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more