Proper efficiency and tradeoffs in multiple criteria and stochastic optimization

Engau, Alexander (2017) Proper efficiency and tradeoffs in multiple criteria and stochastic optimization. Mathematics of Operations Research, 42 (1). pp. 119-134. ISSN 0364-765X

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Abstract

The mathematical equivalence between linear scalarizations in multiobjective programming and expected-value functions in stochastic optimization suggests to investigate and establish further conceptual analogies between these two areas. In this paper, we focus on the notion of proper efficiency that allows us to provide a first comprehensive analysis of solution and scenario tradeoffs in stochastic optimization. In generalization of two standard characterizations of properly efficient solutions using weighted sums and augmented weighted Tchebycheff norms for finitely many criteria, we show that these results are generally false for infinitely many criteria. In particular, these observations motivate a slightly modified definition to prove that expected-value optimization over continuous random variables still yields bounded tradeoffs almost everywhere in general. Further consequences and practical implications of these results for decision-making under uncertainty and its related theory and methodology of multiple criteria, stochastic and robust optimization are discussed.

Item Type:
Journal Article
Journal or Publication Title:
Mathematics of Operations Research
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1700/1706
Subjects:
ID Code:
90193
Deposited By:
Deposited On:
09 Feb 2018 08:48
Refereed?:
Yes
Published?:
Published
Last Modified:
09 Jul 2020 05:46