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Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Proper efficiency and tradeoffs in multiple criteria and stochastic optimization
AU - Engau, Alexander
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - proper efficiency
KW - tradeoffs
KW - multicriteria optimization
KW - multiobjective programming
KW - stochastic optimization
KW - stochastic programming
KW - robust optimization
KW - linear scalarization
KW - weighted sum method
KW - augmented Tchebycheff norm
KW - expected value function
KW - decision making under uncertainty
U2 - 10.1287/moor.2016.0796
DO - 10.1287/moor.2016.0796
M3 - Journal article
VL - 42
SP - 119
EP - 134
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
SN - 0364-765X
IS - 1
ER -