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Stability results for approximately efficient solutions

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Abstract

We introduce a concept for approximately efficient solutions in vector optimization and compare it with another recent concept given in [8]. Further, we study relations between the set of approximately efficient solutions of a vector optimization problem and the approximate solutions of a corresponding parametric surrogate optimization problem. Finally, we prove stability properties for the scalar surrogate problem.

Zusammenfassung

Wir führen ein Konzept für Näherungslösungen in der Vektoroptimierung ein und vergleichen dieses mit einem neuen Konzept aus [8]. Weiterhin untersuchen wir Beziehungen zwischen der Menge der Näherungslösungen eines Vektoroptimierungsproblems und den Näherungslösungen eines entsprechenden parametrischen Ersatzproblems. Schließlich beweisen wir Stabilitätseigenschaften des skalaren Ersatzproblems.

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Tammer, C. Stability results for approximately efficient solutions. OR Spektrum 16, 47–52 (1994). https://doi.org/10.1007/BF01719703

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Key words

  • Vector optimization
  • approximately efficient solutions
  • stability

Schlüsselwörter

  • Vektoroptimierung
  • Näherungslösungen
  • Stabilität