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

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

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An Erratum to this article was published on 01 March 1997

Abstract

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).

Zusammenfassung

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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Author information

Authors and Affiliations

  1. Fachbereich IV, Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Federal Republic of Germany

    R. Horst

  2. VIEN TOAN HOC Institute of Mathematics, Bò Ho, P. O. Box 631, Hanoi, Vietnam

    N. V. Thoai

Authors
  1. R. Horst
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  2. N. V. Thoai
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Additional information

This paper was accomplished while the second author was on leave with the Alexander von Humboldt-Foundation at the University of Trier.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02684407.

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Horst, R., Thoai, N.V. Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems. Computing 42, 271–289 (1989). https://doi.org/10.1007/BF02239754

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  • DOI: https://doi.org/10.1007/BF02239754

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