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Alternating proximal gradient descent for nonconvex regularised problems with multiconvex coupling terms

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VMVW01 - Variational methods, new optimisation techniques and new fast numerical algorithms

Co-author: Pauline Tan

There has been an increasing interest in constrained nonconvex  regularized block multiconvex optimization problems. We introduce an  approach that effectively exploits the multiconvex structure of the coupling term and enables complex application-dependent regularization terms to be used. The proposed Alternating Structure-Adapted Proximal gradient descent algorithm enjoys simple well defined updates. Global convergence of the algorithm to a critical point is proved using the so-called Kurdyka-Lojasiewicz  property. What is more, we prove that a large class of useful objective functions obeying our assumptions are subanalytic and thus satisfy the Kurdyka-Lojasiewicz property. Finally, present an application of the algorithm to big-data air-born sequences of images.



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