A general theory of dual optimization problems. II: On the perturbational dual problem corresponding to an unperturbational dual problem
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Abstract
Distinguishing between a problem and its instances, we redefine the perturbational dual problem corresponding to an unperturbational dual problem, by means of explicit formulas, instead of “the scheme” of “formal replacements” of [15]. We show the relations between some main perturbational dual problems and the perturbational dual problems corresponding to some main unperturbational dual problems.
Key words
49D30 (Duality Theory, Lagrange Theory) 90C48 (Programming in Abstract Spaces) 90C31 (Sensitivity, Parametric Programming)Zusammenfassung
In der vorliegenden Arbeit wird eine neue Definition für das zu einem “unperturbational” (das heißt, ohne Hilfe von Störungen des primalen Problems definierte) duale Problem entsprechende “perturbational” (d. h., in Bezug auf eine Störung des primalen Problems definierte) duale Optimierungsproblem gegeben und studiert. Anders als in [15] beruht diese Definition nicht auf einem “Schema formaler Ersetzungen”, sondern geschieht anhand von expliziten Formeln.
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