Journal of Global Optimization

, Volume 22, Issue 1–4, pp 49–57 | Cite as

A class of problems where dual bounds beat underestimation bounds

  • Mirjam Dür


We investigate the problem of minimizing a nonconvex function with respect to convex constraints, and we study different techniques to compute a lower bound on the optimal value: The method of using convex envelope functions on one hand, and the method of exploiting nonconvex duality on the other hand. We investigate which technique gives the better bound and develop conditions under which the dual bound is strictly better than the convex envelope bound. As a byproduct, we derive some interesting results on nonconvex duality.

Nonconvex duality Dual bounds Convex underestimation 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Mirjam Dür
    • 1
  1. 1.Department of StatisticsVienna University of Economics and Business AdministrationViennaAustria

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