Description
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
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.
Book Information
ISBN 9781611976984
Author Coralia Cartis
Format Hardback
Page Count 529
Imprint Society for Industrial & Applied Mathematics,U.S.
Publisher Society for Industrial & Applied Mathematics,U.S.
Weight(grams) 1344g
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.
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.
Book Information
ISBN 9781611976984
Author Coralia Cartis
Format Hardback
Page Count 529
Imprint Society for Industrial & Applied Mathematics,U.S.
Publisher Society for Industrial & Applied Mathematics,U.S.
Weight(grams) 1344g
