Definition and Characterization of Geoffrion Proper Efficiency for Real Vector Optimization with Infinitely Many Criteria

Alexander Engau ()
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Alexander Engau: University of Colorado Denver

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 2, No 7, 439-457

Abstract: 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.

Keywords: Proper efficiency; Multicriteria optimization; Multiobjective programming; Infinitely many criteria; Weighted-sum method; Tchebycheff norm; Scalarization; 90C29; 90C48; 65K10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-014-0608-5

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