Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives (MOS-SIAM Series on Optimization) - Hardcover

Coralia Cartis (author); Nicholas I. M. Gould (author)

Hardcover

ISBN 10: 1611976987 ISBN 13: 9781611976984

Publisher: SIAM - Society for Industrial and Applied Mathematics, 2022

Synopsis

One of the most popular ways to assess the "effort" needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions―and given access to problem-function values and derivatives of various degrees―how many evaluations might be required to approximately solve the problem?

Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book

• on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems,
• to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and
• to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view.

This is the go-to book for those interested in solving nonconvex problems. It is suitable for advanced undergraduate and graduate students in courses on Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

About this title

About the Author

Coralia Cartis has been Associate Professor in Numerical Optimization at the Mathematical Institute, University of Oxford since 2013, and a Turing fellow at the Alan Turing Institute for Data Science since 2016. Her research interests include the development and analysis of nonlinear optimization algorithms, with particular emphasis on complexity/global rates of convergence, and diverse applications of optimization from climate modelling to signal processing and machine learning.

Nicholas I. M. Gould is a Senior Fellow at the STFC-Rutherford Appleton Laboratory in Oxfordshire, and a visiting professor at the Universities of Edinburgh and Oxford. His research interests include the theory and practice of optimization methods, numerical linear algebra, large-scale scientific computation, and the links between these fields.

Philippe L. Toint has been the co-director of the Numerical Analysis Unit and director of the Transportation Research Group at the University of Namur since 1979. His research interests include numerical optimization, numerical analysis, and transportation.

Edition details

• Publisher: SIAM - Society for Industrial and Applied Mathematics
• Publication date: 2022
• Language: English
• ISBN 10: 1611976987
• ISBN 13: 9781611976984
• Binding: Hardcover
• Number of pages: 529