Stochastic Optimization: Approximation Algorithms and Asymptotic Analysis

点击翻译按钮获取中文摘要

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.