Optimization Algorithms for Problems with Stochastic Dominance Constraints

具有随机优势约束问题的优化算法

• 批准号: 0727532
• 负责人: Tito Homem-de-Mello
• 金额: $ 42.45万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0727532&HistoricalAwards=false
• 关键词: Optimization; Algorithms; Problems; Stochastic; Dominance

This proposed research provides funding for the study of optimization problems where the uncertainty intrinsic to the constraints in the problem is modeled using a concept known as stochastic dominance. Two optimization problems which will receive an early focus in the research are the uncertain linear and uncertain semidefinite programs under a second-order linear stochastic dominance concept, which constitutes a particular way to model multi-dimensional stochastic orders. Efficient algorithms for such problems will be constructed. In addition, a duality theory that allows explicit construction of dual functions associated with the solution of such problems will be developed. More general stochastic orders and the solvability of corresponding optimization problems will be analyzed. The research will also address the situation where the support of the random entities in the stochastic dominance constraints is not finite or is very large, so that sampling based approaches are required. Finally, a study of stochastic entities with random parameters and their applications may be conducted within the context of stochastic dominance.If successful, the proposed research will address the fundamental problem of optimizing a system where some components are not known with certainty, which has applications in many areas, including operations research, statistics and finance. The work will help to develop a better understanding of the benefits and drawbacks of using the concept of stochastic dominance --- which has proven to be of capital importance in many areas, ranging from economics to epidemiology --- in an optimization problem. One goal of this research is to develop algorithms for such problems, the availability of which will result in better modeling of parameter uncertainty in stochastic models. The proposed research builds upon two unrelated areas (optimization and stochastic dominance) and it is expected to promote a cross-fertilization of ideas that can potentially lead to further advances in both areas, while allowing for improved modeling abilities of application problems. This combination of different areas will also lead to the development of new graduate courses and the dissemination of ideas through a set of lecture notes on the topic.

这项拟议的研究为研究优化问题提供了资金，其中使用称为随机优势的概念对问题的约束进行了固有的固有。在研究中将早期重点的两个优化问题是在二阶线性随机优势概念下的不确定线性和不确定的半限定程序，这构成了模拟多维随机顺序的一种特殊方法。将构建用于此类问题的有效算法。此外，将开发出与解决方案相关的双重函数的二元理论。将分析更通用的随机顺序和相应优化问题的可溶性。该研究还将解决随机支配约束中随机实体的支持不是有限或非常大的情况，因此需要基于抽样的方法。最后，对具有随机参数的随机实体及其应用的研究可能是在随机优势的背景下进行的。如果成功，则拟议的研究将解决优化某些组件的基本问题，在该系统中，某些组件尚不确定，该系统在许多领域中都有应用，包括运营研究，统计，统计，统计，统计，和金融。这项工作将有助于更好地理解使用随机支配地位的概念的收益和缺点 - 事实证明，这在许多领域都具有资本重要性，从经济学到流行病学 - 在优化问题中。这项研究的目标之一是为这些问题开发算法，其可用性将导致随机模型中参数不确定性的更好建模。拟议的研究建立在两个无关的领域（优化和随机优势）上，并有望促进思想的交叉侵入，这些思想有可能在这两个领域中进一步进步，同时允许提高应用程序问题的建模能力。不同领域的这种组合还将通过一系列关于该主题的讲义来发展新的研究生课程和思想的传播。