Abstract
Following a comprehensive bibliography recently published in this journal, we review major results in fractional programming. The emphasis is on structural properties of fractional programs and their algorithmic implications. We limit the discussion to those types of ratio optimization problems for which we see a significant interest in the applications. It is attempted to provide a theoretical framework for future research in this area.
Zusammenfassung
Im Anschluß an die kürzliche Veröffentlichung einer umfassenden Bibliographie zur Quotientenprogrammierung in dieser Zeitschrift wird in der vorliegenden Arbeit ein überblick über wichtige Ergebnisse auf diesem Gebiet der nichtlinearen Programmierung gegeben. Es stehen dabei strukturelle Eigenschaften von Quotientenprogrammen sowie deren Bedeutung für Lösungsverfahren im Mittelpunkt der Untersuchung. Die Diskussion beschränkt sich auf solche Quotientenprogramme, die für die Anwendungen von größerem Interesse sind. Es wird in der Arbeit versucht einen theoretischen Rahmen zu entwickeln, der für weitere Untersuchungen zur Quotientenprogrammierung hilfreich sein kann.
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This research was supported by J.D. Muir Fund, Faculty of Business, University of Alberta.
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Schaible, S. Fractional programming. Zeitschrift für Operations Research 27, 39–54 (1983). https://doi.org/10.1007/BF01916898
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DOI: https://doi.org/10.1007/BF01916898