Proximal Newton-Type Methods for Minimizing Composite Functions
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type meth...
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| Published in | SIAM journal on optimization Vol. 24; no. 3; pp. 1420 - 1443 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1052-6234 1095-7189 |
| DOI | 10.1137/130921428 |
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| Abstract | We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing smooth functions, even when search directions are computed inexactly. Many popular methods tailored to problems arising in bioinformatics, signal processing, and statistical learning are special cases of proximal Newton-type methods, and our analysis yields new convergence results for some of these methods. [PUBLICATION ABSTRACT] |
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| AbstractList | We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing smooth functions, even when search directions are computed inexactly. Many popular methods tailored to problems arising in bioinformatics, signal processing, and statistical learning are special cases of proximal Newton-type methods, and our analysis yields new convergence results for some of these methods. [PUBLICATION ABSTRACT] We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing smooth functions, even when search directions are computed inexactly. Many popular methods tailored to problems arising in bioinformatics, signal processing, and statistical learning are special cases of proximal Newton-type methods, and our analysis yields new convergence results for some of these methods. |
| Author | Saunders, Michael A. Lee, Jason D. Sun, Yuekai |
| Author_xml | – sequence: 1 givenname: Jason D. surname: Lee fullname: Lee, Jason D. – sequence: 2 givenname: Yuekai surname: Sun fullname: Sun, Yuekai – sequence: 3 givenname: Michael A. surname: Saunders fullname: Saunders, Michael A. |
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| SubjectTerms | Approximation Bioinformatics Composite functions Convergence Convex analysis Handles Learning Mathematical analysis Mathematical models Methods Optimization Signal processing |
| Title | Proximal Newton-Type Methods for Minimizing Composite Functions |
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