Collaborative Research: Semi-Infinite Probabilistic Optimization

合作研究：半无限概率优化

• 批准号: 0303728
• 负责人: Darinka Dentcheva
• 金额: $ 13.52万
• 依托单位: Stevens Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0303728&HistoricalAwards=false
• 关键词: Collaborative; Research; Semi; Infinite; Probabilistic

The proposed research aims at improving the mathematical foundations of nonlinear stochastic optimization under high uncertainty. We plan to develop new models involving infinitely many constraints on functions characterizing distributions of random outcomes. In particular we will consider semi-infinite optimization problems with constraints on the probability distribution functions and their transforms, e.g., excess/shortfall measures. We will analyze the structure of these models and we will develop optimality conditions and duality theory. Further we will carry out an analysis of stability and develop new approximation methods for these problems. These theoretical advances will serve as a basis for developing new numerical methods for solving optimization problems under high uncertainty.In many practical problems optimal decisions must be made under uncertain conditions. Investment planning is one example, but problems of this type occur in telecommunications, insurance and finance, electricity generation and distribution, supply chain management, manufacturing, and in the military, as well as in other areas. Existing techniques do not work well when there are events that are very unlikely to occur but which cannot be safely ignored. This project will provide new mathematical tools and numerical methods to deal with such problems.

该研究旨在改善高不确定性下非线性随机优化的数学基础。我们计划开发新的模型，涉及无限多的约束函数的特征分布的随机结果。特别地，我们将考虑对概率分布函数及其变换具有约束的半无限优化问题，例如，超额/短缺措施。我们将分析这些模型的结构，我们将开发最优性条件和对偶理论。此外，我们将进行稳定性分析，并为这些问题开发新的近似方法。这些理论上的进展将为发展新的数值方法解决高度不确定性下的优化问题奠定基础。在许多实际问题中，最优决策必须在不确定条件下进行。投资规划就是一个例子，但这类问题发生在电信、保险和金融、发电和配电、供应链管理、制造业、军事以及其他领域。当存在极不可能发生但不能安全地忽略的事件时，现有技术不能很好地工作。该项目将提供新的数学工具和数值方法来处理这些问题。