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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.

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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Authors and Affiliations

  1. Department of Mathematics, INCREST, Bd. Pacii 220, 79622, Bucharest

    I. Singer

  2. Institute of Mathematics, Str. Academiei, 14, 70109, Bucharest, Romania

    I. Singer

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  1. I. Singer
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Invited talk at the 12 Symposium on Operations Research, Passau, September 1987.

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Singer, I. A general theory of dual optimization problems. II: On the perturbational dual problem corresponding to an unperturbational dual problem. ZOR - Methods and Models of Operations Research 33, 241–258 (1989). https://doi.org/10.1007/BF01423334

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  • DOI: https://doi.org/10.1007/BF01423334

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