Optimization for Learning and Control

1Introduction

This book will take you on a journey through the fascinating field of optimization, where we explore techniques for designing algorithms that can learn and adapt to complex systems. Whether you are an engineer, a scientist, or simply curious about the world of optimization, this book is for you. We will start with the basics of optimization and gradually build up to advanced techniques for learning and control. By the end of this book, you will have a solid foundation in optimization theory and practical tools to apply to real‐world problems. In this opening, we informally introduce problems and concepts, and we will explain their close interplay with simple formulations and examples. Chapters 2–13 will explore the topic with more rigor, and we end this chapter with an outline of the remaining content of the book.

1.1 Optimization

Optimization is about choosing a best option from a set of available alternatives based on a specific criterion. This concept applies to a range of disciplines, including computer science, engineering, operations research, and economics, and has a long history of conceptual and methodological development. One of the most common optimization problems is of the form

(1.1)

with variable . This is called a nonlinear least‐squares problem, ...