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Variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function
Abstract : We consider the minimization of a function $G$ defined on $R^N$, which is the sum of a (non necessarily convex) differentiable function and a (non necessarily differentiable) convex function. Moreover, we assume that $G$ satisfies the Kurdyka-Lojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose an acceleration strategy based on the use of variable metrics and of the Majorize-Minimize principle. We give conditions under which the sequence generated by the resulting Variable Metric Forward-Backward algorithm converges to a critical point of $G$. Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application.
Cited literature [43 references]
https://hal.archives-ouvertes.fr/hal-00789970
Contributor : Emilie Chouzenoux Connect in order to contact the contributor
Submitted on : Tuesday, February 19, 2013 - 10:38:01 AM
Last modification on : Saturday, January 15, 2022 - 3:56:42 AM
Long-term archiving on: : Monday, May 20, 2013 - 4:00:19 AM
Contributor : Emilie Chouzenoux Connect in order to contact the contributor
Submitted on : Tuesday, February 19, 2013 - 10:38:01 AM
Last modification on : Saturday, January 15, 2022 - 3:56:42 AM
Long-term archiving on: : Monday, May 20, 2013 - 4:00:19 AM
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