Derivative-Free and Blackbox Optimization
Description
The second edition of Derivative-Free and Blackbox Optimization offers a comprehensive introduction to the field of optimization when derivatives are unavailable, unreliable, or impractical. Whether you're a student, instructor, or self-learner, this book is designed to guide you through both the foundations and advanced techniques of derivative-free and blackbox optimization. This new edition features significantly expanded exercises, updated and intuitive notation, over 30 new figures, and a wide range of pedagogical enhancements aimed at making complex concepts accessible and engaging. The book is structured into five parts. Part 1 established foundational principles, including an expanded chapter on proper benchmarking. Parts 2, 3, and 4, take an in-depth look at heuristics, direct search, and model based approaches (respectively). Part 5 extends these approaches to specialised settings. Finally, a new appendix contributed by Sébastien Le Digabel, details several real-world applications of blackbox optimization, and links to software for each application. Whether used in the classroom or for independent exploration, this book is a powerful resource for understanding and applying optimization methods - no gradients required.
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Persons
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 postdoctoral researcher at Rice University.
Dr. Warren Hare is a Professor of Mathematics at the University of British Columbia, Okanagan Campus. His research interests include numerical analysis and algorithm design, particularly for derivative-free optimisation. He obtained his Ph.D. in optimization from Simon Fraser University and worked as postdoctoral researcher at the Instituto de Mathemática Pura e Applicada and McMaster University.
Content
Part 1. Introduction and Background Material.- Introduction: Tools and Challenges in Derivative-Free and Blackbox Optimization.- Mathematical Background.- The Beginnings of DFO Algorithms.- Comparing Optimization Methods.- Some Remarks on DFO.- Part 2. Popular Heuristic Methods.- Genetic Algorithms.- Nelder-Mead.- Further Remarks on Heuristics.- Part 3. Direct Search Methods.- Positive Bases and Nonsmooth Optimization.- Generalised Pattern Search.- Mesh Adaptive Direct Search.- Variables and Constraints.- Further Remarks on Direct Search Methods.- Part 4. Model-Based Methods.- Assessing Model Quality.- Simplex Gradients and Hessians.- Model-Based Descent.- Model-Based Trust Region.- Further Remarks on Model-Based Methods.- Part 5. Extensions and Refinements.- Optimization Using Surrogates and Models.- Biobjective Optimization.- Final Remarks on DFO/BBO.- Appendix A. Blackbox Test Problems.- Appendix. Answers to Every Fourth Exercise.- Bibliography.- Index.