Stochastic Optimization: Approximation Algorithms and Asymptotic Analysis

由于新时代技术的快速进步，现实世界的系统已经拥抱了越来越大的复杂性。它们不仅会在随机干扰下不断变化，而且还会经历某些切换过程，偶尔会跳跃变化以影响系统的状态，从而呈现出另一种不确定性。为了满足无线通信、信号处理、制造、金融和经济等领域的需求，本项目旨在为这类系统设计有效的计算方法和分析性质。该项目提出了考虑噪声测量和随机环境的算法，用于移动通信和金融市场分析中的新兴应用。在涉及额外环境变量的追逐-逃避游戏的激励下，该项目开发了偶尔和随机切换游戏的数值程序，具有潜在的国土安全应用。为了执行只有使用传感器获得的数据才能获得的识别任务，例如在汽车工程和医疗应用中，将研究使用量化数据的识别算法。为了能够描述复杂系统及其固有的不确定性和随机环境，本项目还强调对随机过程的内在属性的理解，包括扩散特征和跳跃特征。所提出的研究将带来新的见解，并推动随机优化方法的发展。

Owing to the rapid advances in technology in the new era, real-world systems have embraced an ever-expanding complexity. Not only do they vary continuously subject to random disturbances, but also they experience certain switching processes, jump-changing occasionally to affect the systems' states, presenting another fold of uncertainty. In response to the needs in wireless communications, signal processing, manufacturing, finance, and economics, this project aims to design efficient computational methods and analytic properties for such systems. The project presents algorithms taking into consideration noisy measurements and random environments for emerging applications in mobile communications and financial market analysis. Motivated by pursuit-evasion games that involve additional environmental variables, this project develops numerical procedures for games with occasional and random switching, with potential applications to homeland security. To carry out identification tasks where only data obtained using sensors are available, as in automotive engineering and medical applications, identification algorithms using quantized data will be examined. To be able to describe complex systems and their inherent uncertainty and random environment, this project also emphasizes the understanding of the intrinsic properties of random processes, including both diffusive features and jump characteristics. The proposed research will yield new insight, and advance the state of the art of stochastic optimization methods.