A proximal iterative approach to a non-convex optimization problem

Abstract : We consider a variable Krasnosel'skii-Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping proxλf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula xk+1=(1−αk)xk+αkproxλkfxk, where (αk) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition.
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https://hal.univ-antilles.fr/hal-00778175
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Submitted on : Friday, January 18, 2013 - 8:01:03 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

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Abdellatif Moudafi. A proximal iterative approach to a non-convex optimization problem. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2010, 72 (2), pp.704-709. ⟨10.1016/j.na.2009.07.011⟩. ⟨hal-00778175⟩

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