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Computational Optimization: Success in Practice: Textbooks in Mathematics

Autor Vladislav Bukshtynov
en Limba Engleză Hardback – 17 feb 2023
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.
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Specificații

ISBN-13: 9781032229478
ISBN-10: 1032229470
Pagini: 414
Ilustrații: 141 Line drawings, color; 141 Illustrations, color
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.84 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics


Public țintă

Postgraduate, Professional, and Undergraduate Advanced

Cuprins

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.

Notă biografică

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.

Descriere

This textbook offers a guided tutorial reviewing the theoretical fundamentals while going through the practical examples used for constructing the computational frame, applied to various real-life models.