Accelerated and Inexact Forward-Backward Algorithms
We propose a convergence analysis of accelerated forward-backward splitting methods for composite function minimization, when the proximity operator is not available in closed form, and can only be computed up to a certain precision. We prove that the $1/k^2$ convergence rate for the function values...
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| Veröffentlicht in: | SIAM journal on optimization 2013-01, Vol.23 (3), p.1607-1633 |
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| container_title | SIAM journal on optimization |
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| creator | Villa, Silvia Salzo, Saverio Baldassarre, Luca Verri, Alessandro |
| description | We propose a convergence analysis of accelerated forward-backward splitting methods for composite function minimization, when the proximity operator is not available in closed form, and can only be computed up to a certain precision. We prove that the $1/k^2$ convergence rate for the function values can be achieved if the admissible errors are of a certain type and satisfy a sufficiently fast decay condition. Our analysis is based on the machinery of estimate sequences first introduced by Nesterov for the study of accelerated gradient descent algorithms. Furthermore, we give a global complexity analysis, taking into account the cost of computing admissible approximations of the proximal point. An experimental analysis is also presented. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/110844805 |
| format | Article |
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| subjects | Algorithms Approximation Computing costs Convergence Cost analysis Estimates Exact solutions Laboratories Machine learning Mathematical analysis Optimization |
| title | Accelerated and Inexact Forward-Backward Algorithms |
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