Information driven optimization methods in control systems, signal processing, telecommunications and stochastic finance.

摘要

This dissertation attempts to unify a seemingly diverse set of optimization algorithms using the common thread of information utilization. The span of treated algorithms ranges from curve fitting procedures in their simplest steepest descent form, to genetic algorithms and their variations.; The optimization techniques play a very important role and they appear in every aspect of the modern systems design: from the design of the initial system architecture through the system parameter optimization; to the ability of the system to track and adapt to changes in the environment. Motivation for theoretical developments in this dissertation work came from a very diverse set of problems: (1) Thyristor Controlled Series Capacitor (TCSC) placement in the wide area power networks; (2) Combined problem of security selection and portfolio optimization; (3) Capacity optimal filtering for discrete multi-tone transmission systems (such as ADSL); and, (4) Linear systems with multiplicative noise and their applications to optimization (such as dithered steepest descent).; Research proposed in this dissertation is geared towards gaining a deeper understanding of common optimization algorithms, finding connections between them, and using these connections to create new classes of hybrid algorithms which borrow benefits of their parents.