Abstract
We consider the minimization of a function G defined on RN , which is the sum of a (not necessarily convex) differentiable function and a (not necessarily differentiable) convex function. Moreover, we assume that G satisfies the Kurdyka–Łojasiewicz 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.
Original language  English 

Pages (fromto)  107–132 
Number of pages  26 
Journal  Journal of Optimization Theory and Applications 
Volume  162 
Issue number  1 
DOIs  
Publication status  Published  Jul 2014 
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Audrey Repetti
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics  Associate Professor
Person: Academic (Research & Teaching)