A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and lo...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 40; no. 1; pp. 85 - 118
Main Author: Schiela, Anton
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.01.2019
Taylor & Francis Ltd
Subjects:
Algorithms
cubic regularization
Function space
Non-convex optimization
Optimization
optimization in function space
Regularization
Resorts & spas
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1499114