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Emilie Chouzenoux (emilie.chouzenouxunivmlv.fr) 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 KurdykaLojasiewicz property. Such a problem can be solved with the ForwardBackward 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 MajorizeMinimize principle. We give conditions under which the sequence generated by the resulting Variable Metric ForwardBackward algorithm converges to a critical point of $G$. Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application. Keywords: Nonconvex optimization ; Nonsmooth optimization ; MajorizeMinimize algorithm ; ForwardBackward algorithm ; Image reconstruction ; Proximity operator Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF] Entry Submitted: 01/29/2013 Modify/Update this entry  
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