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arXiv · 1405.1357

Splitting methods with variable metric for KL functions

Pierre Frankel·Guillaume Garrigos·Juan Peypouquet
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Abstract

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method with variable metric and relative errors. As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailled.

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Pierre Frankel, Guillaume Garrigos, Juan Peypouquet. 2014-07-07. Splitting methods with variable metric for KL functions. https://doi.org/10.1007/s10957-014-0642-3

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