, Volume 9, Issue 3, pp 153–159 | Cite as

Outer approximation by polyhedral convex sets

  • R. Horst
  • Ng. V. Thoai
  • H. Tuy
Theoretical Papers


This paper deals with outer approximation methods for solving possibly multiextremal global optimization problems. A general theorem on convergence is presented and new classes of outer approximation methods using polyhedral convex sets are derived. The underlying theory is then related to the cut map-separator theory of Eaves and Zangwill. Two constraint dropping strategies are deduced.


Approximation Method Global Optimization General Theorem Global Optimization Problem Underlying Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Diese Arbeit befaßt sich mit äußeren Approximationsverfahren zur Lösung von möglicherweise multiextremalen globalen Optimierungsproblemen. Ein allgemeiner Konvergenzsatz wird vorgestellt, aus dem sich neue Klassen von Schnittebenenverfahren ableiten lassen. Schließlich wird die dargestellte Theorie in Bezug gesetzt zur Schnittabbildung-Separatoren-Theorie von Eaves und Zangwill. Zwei Strategien zur Reduzierung der Nebenbedingungen werden vorgestellt.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. Horst
    • 1
  • Ng. V. Thoai
    • 2
  • H. Tuy
    • 2
  1. 1.Fachbereich IV - MathematikUniversität TrierTrierFederal Republic of Germany
  2. 2.Institute of MathematicsHanoiVietnam

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