A generic coordinate descent solver for nonsmooth convex optimization

We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual updates and automatically determines which dual variables sh...

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Bibliographic Details
Published inOptimization methods & software pp. 1 - 21
Main Author Fercoq, Olivier
Format Journal Article
LanguageEnglish
Published Taylor & Francis 27.08.2019
Subjects
Mathematics
Optimization and Control
efficient implementation
generic solver
convex optimization
Coordinate descent
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Summary:We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual updates and automatically determines which dual variables should be duplicated. A list of basic functional atoms is pre-compiled for efficiency and a modelling language in Python allows the user to combine them at run time. So, the algorithm can be used to solve a large variety of problems including Lasso, sparse multinomial logistic regression, linear and quadratic programs.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2019.1658758