This textbook offers a guided tutorial that reviews the theoretical fundamentals while going through the practical examples used for constructing the computational frame, applied to various real-life models.
Computational Optimization: Success in Practice will lead the readers through the entire process. They will start with the simple calculus examples of fitting data and basics of optimal control methods and end up constructing a multi-component framework for running PDE-constrained optimization. This framework will be assembled piece by piece; the readers may apply this process at the levels of complexity matching their current projects or research needs.
By connecting examples with the theory and discussing the proper "communication" between them, the readers will learn the process of creating a "big house." Moreover, they can use the framework exemplified in the book as the template for their research or course problems – they will know how to change the single "bricks" or add extra "floors" on top of that.
This book is for students, faculty, and researchers.
Features
- The main optimization framework builds through the course exercises and centers on MATLAB®
- All other scripts to implement computations for solving optimization problems with various models use only open-source software, e.g., FreeFEM
- All computational steps are platform-independent; readers may freely use Windows, macOS, or Linux systems
- All scripts illustrating every step in building the optimization framework will be available to the readers online
- Each chapter contains problems based on the examples provided in the text and associated scripts. The readers will not need to create the scripts from scratch, but rather modify the codes provided as a supplement to the book
This book will prove valuable to graduate students of math, computer science, engineering, and all who explore optimization techniques at different levels for educational or research purposes. It will benefit many professionals in academic and industry-related research: professors, researchers, postdoctoral fellows, and the personnel of R&D departments.
Chapter 1. Introduction to Optimization
Chapter 2. Minimization Approaches for Functions of One Variable
Chapter 3. Generalized Optimization Framework
Chapter 4. Exploring Optimization Algorithms
Chapter 5. Line Search Algorithms
Chapter 6. Choosing Optimal Step Size
Chapter 7. Trust Region and Derivative-Free Methods
Chapter 8. Large-Scale and Constrained Optimization
Chapter 9. ODE-based Optimization
Chapter 10. Implementing Regularization Techniques
Chapter 11. Moving to PDE-based Optimization
Chapter 12. Sharing Multiple Software Environments
Biography
Dr. Vladislav Bukshtynov holds a Ph.D. degree in Computational Engineering & Science from McMaster University. He is an Assistant Professor at the Dept. of Mathematical Sciences of Florida Institute of Technology. He completed a 3-year postdoctoral term at the Dept. of Energy Resources Engineering of Stanford University. He actively teaches and advises students from various fields: applied and computational math, operations research, different engineering majors. His teaching experience includes Multivariable Calculus, Honors ODE/PDE courses for undergrad students; Applied Discrete Math, Linear/Nonlinear Optimization for senior undergrads and graduates. As a researcher, Dr. Bukshtynov leads his research group with several dynamic scientific directions and ongoing collaborations for various cross-institutional and interdisciplinary projects. His current interests lie in but are not limited to the areas of applied and computational mathematics focusing on combining theoretical and numerical methods for various problems in computational/numerical optimization, control theory, and inverse problems.
