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A Primal Heuristic for Nonsmooth Mixed Integer Nonlinear Optimization

In: Facets of Combinatorial Optimization

Author

Listed:
  • Martin Schmidt

    (Leibniz Universität Hannover, Institut für Angewandte Mathematik)

  • Marc C. Steinbach

    (Leibniz Universität Hannover, Institut für Angewandte Mathematik)

  • Bernhard M. Willert

    (Leibniz Universität Hannover, Institut für Angewandte Mathematik)

Abstract

Complex real-world optimization tasks often lead to mixed-integer nonlinear problems (MINLPs). However, current MINLP algorithms are not always able to solve the resulting large-scale problems. One remedy is to develop problem specific primal heuristics that quickly deliver feasible solutions. This paper presents such a primal heuristic for a certain class of MINLP models. Our approach features a clear distinction between nonsmooth but continuous and genuinely discrete aspects of the model. The former are handled by suitable smoothing techniques; for the latter we employ reformulations using complementarity constraints. The resulting mathematical programs with equilibrium constraints (MPEC) are finally regularized to obtain MINLP-feasible solutions with general purpose NLP solvers.

Suggested Citation

  • Martin Schmidt & Marc C. Steinbach & Bernhard M. Willert, 2013. "A Primal Heuristic for Nonsmooth Mixed Integer Nonlinear Optimization," Springer Books, in: Michael Jünger & Gerhard Reinelt (ed.), Facets of Combinatorial Optimization, edition 127, pages 295-320, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-38189-8_13
    DOI: 10.1007/978-3-642-38189-8_13
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