Optimization Principle

Author: Hu Shigeng, Shi Baochang
Publisher:
Publish Date: 2004-06-01
Features: This book provides a systematic treatment of the fundamental content of the so-called infinite-dimensional optimization theory. The book consists of 8 chapters, with the first two chapters summarizing the prerequisite knowledge required to understand the main content of the book, including basic results in functional analysis and nonsmooth analysis. Subsequent chapters elaborate on the fundamental topics of optimization theory: inequality systems and selection theorems, first-order and higher-order optimality conditions, duality theory, vector optimization, etc. On one hand, the book concisely summarizes the standard content of optimization theory, while also introducing numerous recent research findings, including some results by the authors themselves. This part covers some research areas that have attracted widespread attention in recent years, thereby potentially bridging the gap between foundational theory and cutting-edge research for readers with research interests. For senior undergraduate students in mathematics departments and graduate students in related science and engineering fields, the book can serve as a textbook after minor revisions. In the process of contemporary scientific development, the increasingly widespread and urgent need for optimization theory has become a notable trend. For scientists and engineers with such needs, this book will provide useful theoretical tools.