Coordinate descent algorithms

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis...

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Vydané v:	Mathematical programming Ročník 151; číslo 1; s. 3 - 34
Hlavný autor:	Wright, Stephen J.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2015 Springer Nature B.V
Predmet:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Linear equations Machine learning Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Optimization algorithms Studies Theoretical United States > US Parallel numerical computing 49M20 Randomized algorithms 90C25 Coordinate descent
ISSN:	0025-5610, 1436-4646
On-line prístup:	Získať plný text
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Abstract	Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution.
AbstractList	Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution. Issue Title: Special Issue: International Symposium on Mathematical Programming, Pittsburgh, July 2015 Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated Coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution.
Author	Wright, Stephen J.
Author_xml	– sequence: 1 givenname: Stephen J. surname: Wright fullname: Wright, Stephen J. email: swright@cs.wisc.edu organization: Department of Computer Sciences, University of Wisconsin-Madison
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CODEN	MHPGA4
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Snippet	Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate... Issue Title: Special Issue: International Symposium on Mathematical Programming, Pittsburgh, July 2015 Coordinate descent algorithms solve optimization...
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SubjectTerms	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Linear equations Machine learning Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Optimization algorithms Studies Theoretical
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