Abstract
This study tries to develop two new approaches to the numerical solution of Stackelberg problems. In both of them the tools of nonsmooth analysis are extensively exploited; in particular we utilize some results concerning the differentiability of marginal functions and some stability results concerning the solutions of convex programs. The approaches are illustrated by simple examples and an optimum design problem with an elliptic variational inequality.
Zusammenfassung
Diese Arbeit zielt auf eine Entwicklung von neuen Verfahren für die numerische Lösung der Stackelbergproblemen. In beiden vorgeschlagenen Verfahren nützt man die Mittel der nichtglatten Analysis aus. Besonders handelt es sich um eine Charakterisierung der verallgemeinerten Gradienten von marginalen Funktionen und einige StabilitÄtsergebnisse, die die Lösungen von konvexen Programmen betreffen. Die Verfahren sind durch einfache Beispiele und ein Optimum Design Problem mit einer elliptischen Variationsungleichung illustriert.
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Prepared while the author was visiting the Department of Mathematics, University of Bayreuth as a guest of the FSP „Anwendungsbezogene Optimierung und Steuerung“.
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Outrata, J.V. On the numerical solution of a class of Stackelberg problems. ZOR - Methods and Models of Operations Research 34, 255–277 (1990). https://doi.org/10.1007/BF01416737
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DOI: https://doi.org/10.1007/BF01416737