, Volume 42, Issue 2–3, pp 271–289 | Cite as

Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems

  • R. Horst
  • N. V. Thoai


Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).

AMS Subject Classificaiton


Key words

Constrained global optimization concave minimization 

Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen


Zur Lösung konkaver Minimierungsprobleme sind einige (theoretische) Verfahren vorgeschlagen worden; wenig ist über ihr numerisches Verhalten bekannt. In dieser Arbeit werden die drei Methoden „Cone-Splitting”, „Polyhedral Annexation” und „Outer Approximation” zur Steigerung ihrer Effizienz beträchtlich modifiziert. Weiters wird über Implementierung sowie Test und Vergleich an mehr als 100 Beispielen mit bis zu 50 Variablen und 30 Nebenbedingungen (plus Nichtnegativitätsbedingung) berichtet.


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • R. Horst
    • 1
  • N. V. Thoai
    • 2
  1. 1.Fachbereich IV, MathematikUniversität TrierTrierFederal Republic of Germany
  2. 2.VIEN TOAN HOC Institute of MathematicsHanoiVietnam

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