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Splitting methods with variable metric for KL functions

Pierre Frankel(p.frankel30***at***orange.fr)
Guillaume Garrigos(guillaume.garrigos***at***gmail.com)
Juan Peypouquet(juan.peypouquet***at***usm.cl)

Abstract: We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satis es 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.

Keywords: Nonconvex and nonsmooth optimization ; Kurdyka- Lojasiewicz inequality ; Descent methods ; Convergence rates ; Variable metric ; Gauss-Seidel method ; Newton-like method

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Other Topics (Other )

Citation: Submitted at Journal of Optimization Theory and Applications (JOTA).

Download: [PDF]

Entry Submitted: 06/06/2014
Entry Accepted: 06/06/2014
Entry Last Modified: 06/06/2014

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