"Splitting methods with variable metric for KL functions and general convergence rates"

Research areas:
Year:
2015
Type of Publication:
Article
Keywords:
Nonconvex and nonsmooth optimization, Kurdyka Lojasiewicz inequality, Descent methods, Convergence rates, Variable metric, Gauss Seidel method, Newton like method
Authors:
  • P. Frankel
  • G. Garrigos
  • J. Peypouquet
Journal:
Journal of Optimization Theory & Applications
Volume:
165
Number:
3
Pages:
874-900
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 LevenbergMarquardt algorithm is detailled.