A Coordinate Gradient Descent Method for Structured Nonsmooth Optimization

Sangwoon Yun

ISBN 10: 3836478609 / ISBN 13: 9783836478601

Published by VDM Verlag Dr. Müller E.K. Nov 2012, 2012

About this Item

Neuware -Nonsmooth optimization problems are generally considered to be more difficult than smooth problems. Yet, there is an important class of nonsmooth problems that lie in between. In this book, we consider the problem of minimizing the sum of a smooth function and a (block separable) convex function with or without linear constraints. This problem includes as special cases bound-constrained optimization, smooth optimization with L_1-regularization, and linearly constrained smooth optimization such as a large-scale quadratic programming problem arising in the training of support vector machines. We propose a block coordinate gradient descent method for solving this class of structured nonsmooth problems. The method is simple, highly parallelizable, and suited for large-scale applications in signal/image denoising, regression, and data mining/classification. We establish global convergence and, under a local Lipschitzian error bound assumption, local linear rate of convergence for this method. Our numerical experiences suggest that our method is effective in practice. This book is helpful to the people who are interested in solving large-scale optimization problems.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 112 pp. Englisch.

Seller Inventory # 9783836478601

Bibliographic Details

• Title: A Coordinate Gradient Descent Method for Structured Nonsmooth Optimization
• Publisher: VDM Verlag Dr. Müller E.K. Nov 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 3836478609
• ISBN 13: 9783836478601
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

Nonsmooth optimization problems are generally considered to be more difficult than smooth problems. Yet, there is an important class of nonsmooth problems that lie in between. In this book, we consider the problem of minimizing the sum of a smooth function and a (block separable) convex function with or without linear constraints. This problem includes as special cases bound-constrained optimization, smooth optimization with L_1-regularization, and linearly constrained smooth optimization such as a large-scale quadratic programming problem arising in the training of support vector machines. We propose a block coordinate gradient descent method for solving this class of structured nonsmooth problems. The method is simple, highly parallelizable, and suited for large-scale applications in signal/image denoising, regression, and data mining/classification. We establish global convergence and, under a local Lipschitzian error bound assumption, local linear rate of convergence for this method. Our numerical experiences suggest that our method is effective in practice. This book is helpful to the people who are interested in solving large-scale optimization problems.

About the Author

Sangwoon Yun: PhD in Mathematics at University of Washington. Research interest: Convex and nonsmooth optimization, variational analysis. Research Fellow at National University of Singapore.