Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization

• 成果类型: Article
• 署名作者: Engau, Alexander
• 署名单位: Children's Hospital Colorado; University of Colorado System; University of Colorado Anschutz Medical Campus; University of Colorado Denver
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0796
• 发表日期: 2017
• 页码: 119-134
• 关键词: off directions; robust; Respect; definition

摘要

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.