Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization
Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization
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多标准和随机优化中的适当效率和权衡
DOI：
10.1287/moor.2016.0796
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Engau
中科院分区：
文献类型：
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作者：
A. Engau
随机优化中多目标编程和预期值函数中线性标量之间的数学等效性表明，在这两个领域之间研究和建立了进一步的概念类似物。在本文中，我们专注于适当效率的概念，使我们能够对随机优化中的解决方案和方案权衡进行首次全面分析。在使用加权总和和增强加权的Tchebycheff规范的两个标准表征的概括中，对于有限的许多标准，我们表明这些结果通常对于无限多个标准是错误的。特别是，这些观察结果激发了一个稍微修改的定义，以证明对连续随机变量的预期价值优化仍然可以产生几乎所有地方的有限折衷。这些结果在不确定性下对决策的进一步后果和实际含义讨论了多个标准，随机和健壮优化的相关理论和方法。
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.
影响因子：
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作者：
Jonas Ide;E. Köbis;Daishi Kuroiwa;A. Schöbel;C. Tammer
通讯作者：
Jonas Ide;E. Köbis;Daishi Kuroiwa;A. Schöbel;C. Tammer