Journal of Global Optimization

, Volume 32, Issue 3, pp 401–407 | Cite as

On the Liu–Floudas Convexification of Smooth Programs

  • Sanjo Zlobec


It is well known that a twice continuously differentiable function can be convexified by a simple quadratic term. Here we show that the convexification is possible also for every Lipschitz continuously differentiable function. This implies that the Liu–Floudas convexification works for, loosely speaking, almost every smooth program occurring in practice.


Global optimum convexification Lipschitz continuously differentiable function 

AMS Subject Classifications

90C30 90C31 


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  1. 1.
    Davidescu, D.M. M.Sc. Thesis, McGill University, Department of Mathematics and Statistics (in progress).Google Scholar
  2. 2.
    Floudas, C.A. 2000Deterministic Global OptimizationKluwer Academic PublishersDordrechtGoogle Scholar
  3. 3.
    Liu, W.B., Floudas, C.A. 1993A remark on the GOP algorithm for global optimizationJournal of Global Optimization3519521CrossRefGoogle Scholar
  4. 4.
    Nocedal, J., Wright, S.J. 1999Numerical OptimizationSpringer Series in Operations ResearchNew YorkGoogle Scholar
  5. 5.
    Winston, W.L., Venkataramanan,  2003Introduction to Mathematical Programming4Brooks/ColePacific Grove, CAGoogle Scholar
  6. 6.
    Zlobec, S. 2001Stable Parametric ProgrammingKluwer Academic PublishersDordrechtGoogle Scholar
  7. 7.
    Zlobec, S. 2003Estimating convexifiers in continuous optimizationMathematical Communications8129137Google Scholar
  8. 8.
    Zlobec, S. 2004Saddle-point optimality: A look beyond convexityJournal of Global Optimization2997112CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcGill UniversityQuebecCanada

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