Definition and characterization of Geoffrion proper efficiency for real vector optimization with infinitely many criteria

Engau, Alexander (2015) Definition and characterization of Geoffrion proper efficiency for real vector optimization with infinitely many criteria. Journal of Optimization Theory and Applications, 165 (2). pp. 439-457. ISSN 0022-3239

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Abstract

The concept and characterization of proper efficiency is of significant theoretical and computational interest, in multiobjective optimization and decision-making, to prevent solutions with unbounded marginal rates of substitution. In this paper, we propose a slight modification to the original definition in the sense of Geoffrion, which maintains the common characterizations of properly efficient points as solutions to weighted sums or series and augmented or modified weighted Tchebycheff norms, also if the number of objective functions is countably infinite. We give new proofs and counterexamples which demonstrate that such results become invalid for infinitely many criteria with respect to the original definition, in general, and we address the motivation and practical relevance of our findings for possible applications in stochastic optimization and decision-making under uncertainty.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Optimization Theory and Applications
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
90194
Deposited By:
Deposited On:
08 Feb 2018 14:44
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Jul 2020 03:48