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Emilie Chouzenoux (emilie.chouzenouxupem.fr) Abstract: A number of recent works have emphasized the prominent role played by the KurdykaLojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of a non necessarily convex differentiable function and a non necessarily differentiable or convex function. The latter function is expressed as a separable sum of functions of blocks of variables. Such an optimization problem can be addressed with the ForwardBackward algorithm which can be accelerated thanks to the use of variable metrics derived from the MajorizeMinimize principle. We propose to combine the latter acceleration technique with an alternating minimization strategy which relies upon a flexible update rule. We give conditions under which the sequence generated by the resulting Block Coordinate Variable Metric ForwardBackward algorithm converges to a critical point of the objective function. An application example to a nonconvex phase retrieval problem encountered in signal/image processing shows the efficiency of the proposed optimization method. Keywords: Nonconvex optimization ; Nonsmooth optimization ; Proximity operator ; MajorizeMinimize algorithm ; Block coordinate descent ; Alternating minimization ; Phase retrieval ; Inverse problems Category 1: Convex and Nonsmooth Optimization Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF] Entry Submitted: 12/20/2013 Modify/Update this entry  
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