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Pré-Publication, Document De Travail Année : 2017

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

Résumé

There has been an increasing interest in constrained nonconvex regularized block biconvex / multiconvex optimization problems. We introduce an approach that effectively exploits the biconvex / multiconvex structure of the coupling term and enables rich 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 for subanalytic functions. Moreover, we prove that a large class of useful objective functions obeying our assumptions are subanalytic and thus satisfy the Kurdyka-Lojasiewicz property.
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Dates et versions

hal-01492846 , version 1 (20-03-2017)
hal-01492846 , version 2 (08-08-2017)

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  • HAL Id : hal-01492846 , version 2

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Mila Nikolova, Pauline Tan. Alternating proximal gradient descent for nonconvex regularised problems with multiconvex coupling terms. 2017. ⟨hal-01492846v2⟩
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