Derivative-Free and Blackbox Optimization

ISBN-13: 9783319689128 / Angielski / Twarda / 2017 / 302 str.

Charles Audet; Warren Hare

Opis

Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region).

Recenzje

"It is a wonderful textbook that can be used entirely or partially to support optimization courses. ... the authors have achieved gloriously their stated goal of 'providing a clear grasp of the foundational concepts in derivative-free and blackbox optimization.' ... I wish that it will find its way somehow to the desks of engineering design optimization practitioners." (Michael Kokkolaras, Optimization and Engineering, Vol. 20, 2019)
"This book targets two audiences: individuals interested in understanding derivative-free optimization (DFO) and blackbox optimization and practitioners who have to solve real-world problems that cannot be approached by traditional gradient-based methods. ... The book is written in a clear style with sufficient details, examples and proofs of theoretical results. The authors pay equal attention to careful theoretical development and analysis of the methods, and to practical details of the algorithms." (Olga Brezhneva, Mathematical Reviews, October, 2018)
"The authors present a comprehensive textbook being an introduction to blackbox and derivative- free optimization. ... The book is for sure a necessary position for students of mathematics, IT or engineering that would like to explore the subject of blackbox and derivative-free optimization. Also the researchers in the area of optimization could treat it as an introductory reading. Finally, the book would be also a good choice for practitionners dealing with such kind of problems." (Marcin Anholcer, zbMATH 1391.90001, 2018)

Spis treści

Part I: Introduction and Background Material.- Introduction: Tools and Challenges.- Mathematical Background.- The Beginnings of DFO Algorithms.- Part I: Some Remarks on DFO.- Part II: Popular Heuristic Methods.- Genetic Algorithms.- Nelder-Mead.- Part II: Further Remarks on Heuristics.- Part III: Direct Search Methods.- Positive bases and Nonsmooth Optimization.- Generalized Pattern Search.- Mesh Adaptive Direct Search.- Part III: Further Remarks on Direct Search Methods.- Part IV: Model-based Methods.- Model-based Descent.- Model-based Trust Region.- Part IV: Further Remarks on Model-based Methods.- Part V: Extensions and Refinements.- Variables and Constraints.- Optimization Using Surrogates and Models.- Biobjective Optimization.- Part V: Final Remarks on DFO/BBO.- Part VI: Appendix: Comparing Optimization Methods.- Solutions to Selected Exercises.

O autorze

Dr. Charles Audet is a Professor of Mathematics at the École Polytechnique de Montréal. His research interests include the analysis and development of algorithms for blackbox nonsmooth optimization, and structured global optimization. He obtained a Ph.D. degree in applied mathematics from the École Polytechnique de Montréal, and worked as a post-doc at Rice University in Houston, Texas.

Dr. Warren Hare received his Ph.D. in Mathematical Optimization from Simon Fraser University.  He complete postdoctoral research at IMPA (Brazil) and McMaster (Canada), before joining the University of British Columbia (Canada).  

Blurb

This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. 

The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I.  Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead).  Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region).  Part V discusses dealing with constraints, using surrogates, and bi-objective optimization.

End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures.  Benchmarking techniques are also presented in the appendix.