Optimization with Uncertainties over Time: Theory and Algorithms

通常，优化只处理静态问题的实例，很少有例外。一些例外包括随机优化和在线优化模型，它们处理目标函数中具有时变不确定性的问题。随机优化预测这些不确定性以随机的方式发生，在线优化允许从一些预先指定的函数类中提取目标函数，同样，以任意的方式。在现有的关于约束优化的文献中，很少有证据表明优化理论或算法处理不确定性同时存在于目标函数和约束中的一类问题。这项提议的目标就是弥合这一差距。本文的研究意义在于：(1)通过发展优化问题的背景理论，批判性地扩展了优化问题的研究领域，纳入了一类具有时变性质的新问题a；(2)为解决时变问题，特别是目前在数据分类、信号处理和网络资源分配方面出现的问题，开辟了一些新的计算模型。拟议的研究有可能影响自主工程系统的设计和运行。它也有可能对支持以人为中心的操作和决策的信息处理系统的研究作出贡献。一些可能受益的工程系统包括：用于跟踪环境和其他变化的监视和监测系统、数据管理系统（包括数据分析、信息检索、决策支持）和无线通信系统，例如移动电话网络。所提出的研究可以提高这些系统的稳定性、可靠性和性能。

Typically, optimization deals exclusively with instances of static problems, with few exceptions. Some exceptions include stochastic optimization and on-line optimization models that treat problems with time-varying uncertainties in the objective functions. Stochastic optimization anticipates that these uncertainties occur in a random fashion and on-line optimization allows for objective functions to be drawn from some pre-specified class of functions, again, in an arbitrary fashion. In the existing literature on constrained optimization, there is litte, if any, evidence of optimization theory or algorithms that treat the class of problems where the uncertainties are both in the objective function and the constraint. The goal of this proposal is to bridge this gap. The significance of the proposed research is twofold: (1) It critically expands the domain of optimization to include a new class of problems a with time-varying nature by developing their background theory; (2) It pioneers some new computational models for solving time-varying problems, and especially those currently arising in data classification, signal processing, and network resource allocations.The proposed research has the potential to impact the design and operation of autonomous engineering systems. It also has the potential to make contribution to the study of information processing systems that support human-centric operations and decisions. Some of the engineered systems that could benefit include: surveillance and monitory systems for tracking environmental and other changes, data management systems (including data analysis, information retrieval, decision support), and wireless communication systems, e.g. mobile phone networks. The proposed research could increase the stability, reliability, and the performance of these systems.