A perturbation approach to the main duality theorem of quadratic geometric programming
نویسندگان
چکیده
Quadratic geometric programming as introduced by Hough and Goforth is an extension of posynomial geometric programming. By using the theory of generalized geometric programming, Jefferson and Scott defined its exact geometric dual. The fundamental relationship between the geometric dual and the original problem is that they assume a common value at their respective optima. This result formally stated as the main duality theorem is proved in this paper by using a dual perturbation approach and two simple geometric inequalities. As a by-product, the insight provided by this constructive proof establishes a numerically precise dual based solution procedure for quadratic geometric programs. Zusammenfassung." Die quadratische geometrische Optimierung wurde yon Hough und Goforth eingefiihrt und stellt eine Erweiterung der posynomialen geometrischen Optimierung dar. Jefferson und Scott definierten unter Verwendung der veraUgemeinerten geometrischen Optimierung ein duales Programm und leiteten Dualitiitsbeziehungen ab, u. a. die Ubereinstimmung der Optimalwerte des primalen und dualen Programms. Letzteres Resultat wird in der vorliegenden Arbeit unter Verwendung eines dualen St6rproblems und zweier einfachen geometrischen Ungleichungen hergeleitet. Gleichzeitig macht die Beweismethode es m6glich, ein Verfahren zur L6sung quadratischer geometrischer Optimierungsprobleme anzugeben.
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ورودعنوان ژورنال:
- Zeitschr. für OR
دوره 31 شماره
صفحات -
تاریخ انتشار 1987