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A note on the continuity of the solution set of special dual optimization problems

  • B. Kummer
Chapter
Part of the Mathematical Programming Studies book series (MATHPROGRAMM, volume 10)

Abstract

In this paper dual programs of convex optimization problems having a parametric objective function and a fixed linear feasible set are studied. By using some properties of the primal problem the continuity of the dual optimal solution set is proved.

Two examples show the necessity of the suppositions.

Key words

Stability Special Dual Programs Optional Solutions Set Point-to-Set Maps 

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References

  1. [1]
    C. Berge, Topological spaces (MacMillan, New York, 1963).zbMATHGoogle Scholar
  2. [2]
    E. G. Gol’shtein, “Teorija dvoistrennosti v matematitseskom programmirovanie i ee prilozhenija”, Iztsatel’stvo Nauka (Moscow, 1971) [In Russian].Google Scholar
  3. [3]
    W.W. Hogan, “Point-to-set maps in mathematical programming,” SIAM Review 15 (1973) 591–603.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    B. Kummer, “Globale Stabilität quadratischer Optimierungs-probleme,” Wissenschaftliche Zeitschrift der Humboldt-Universität. Naturwissenschaftliche Reihe, (to appear in 1978).Google Scholar

Copyright information

© The Mathematical Programming Society 1979

Authors and Affiliations

  • B. Kummer
    • 1
  1. 1.Der Humboldt UniversitätBerlinGDR

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