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Zeitschrift für Operations Research

, Volume 26, Issue 1, pp 197–209 | Cite as

On abstract duality in mathematical programming

  • R. E. Burkard
  • H. Hamacher
  • J. Tind
Papers Series A: Theory

Abstract

It is shown that duality in mathematical programming can be treated as a purely order theoretic concept which leads to some applications in economics. Conditions for strong duality results are given. Furthermore the underlying sets are endowed with (semi-)linear structures, and the perturbation function of arising linear and integer problems, which include bottleneck problems and extremal problems (in the sense of K. Zimmermann), is investigated.

Keywords

Mathematical Programming Theoretic Concept Extremal Problem Linear Structure Starke 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

In dieser Arbeit wird aufgezeigt, daß Dualitätskonzepte der mathematischen Optimierung in ordnungstheoretischem Rahmen beschrieben werden können. Dies führt u.a. auf neue Anwendungen in der Ökonomie. Ferner werden Bedingungen hergeleitet, unter denen starke Dualitätsaussagen gelten. Sodann werden die zugrundeliegenden Mengen mit algebraischen Strukturen versehen und es werden Dualitätssätze für lineare und ganzzahlige Programme über diesen Mengen bewiesen. Darunter fallen nicht nur die klassischen linearen und ganzzahligen Programme, sondern auch Probleme mit Engpaßzielfunktion und „extremale Probleme“ im Sinne von K. Zimmermann.

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Copyright information

© Physica-Verlag 1982

Authors and Affiliations

  • R. E. Burkard
    • 1
  • H. Hamacher
    • 2
  • J. Tind
    • 3
  1. 1.Institut für MathematikTechnische Universität GrazGraz
  2. 2.Department of Industrial and Systems EngineeringUnviersity of FloridaGainesvilleUSA
  3. 3.Department of Operations ResearchUniversity of AarhusAarhus C

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