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Equivalence of various linearization algorithms for linear fractional programming

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Zusammenfassung

In dieser Arbeit werden vier Algorithmen zur linearen Quotientenoptimierung betrachtet und es wird gezeigt, daß alle vier Linearisierungsverfahren vom Frank Wolfe-Typ sind. Die betrachteten Algorithmen wurden von Isbell und Marlow, Mangasarian, Bitran and Novaes sowie von Bhatt vorgeschlagen. Es wird gezeigt, daß diese Verfahren alle im wesentlichen dieselbe Folge von linearen Programmen erzeugen und damit dieselbe Folge von zulässigen Punkten, die zur Optimallösung führt.

Abstract

This paper considers four algorithms for linear fractional programming and show that they are all Frank Wolfe type linearization algorithms. These algorithms are those proposed by Isbell and Marlow, Mangasarian, Bitran and Novaes; and Bhatt. It is shown that these algorithms all use essentially the same sequence of l.p.s to generate the same sequence of feasible points that leads to the optimal solution.

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Authors and Affiliations

  1. Faculty of Management, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    S. K. Bhatt

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  1. S. K. Bhatt
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Bhatt, S.K. Equivalence of various linearization algorithms for linear fractional programming. ZOR - Methods and Models of Operations Research 33, 39–43 (1989). https://doi.org/10.1007/BF01415516

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  • DOI: https://doi.org/10.1007/BF01415516

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