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By Mr (i: C (k, Hedy (f-mont) Bolte and Reviewed W. W. Breckner


On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. (English summary) Math. Program. 116 (2009), no. 1-2, Ser. B, 5–16. Let f: Rn → R ∪ {+∞} be a proper lower semicontinuous function satisfying the following conditions: (i) infRn f> −∞; (ii) the restriction of f to its domain is continuous. Under the additional assumption that f has a certain property (called the Łojasiewicz property) around its generalized critical points, the authors prove that a bounded sequence (xk)k∈N generated by the proximal algorithm applied to f converges to a generalized critical point of f. This result is completed by specifying the rate of convergence. This rate depends on the value of the so-called Łojasiewicz exponent which can be thought of as a local measure of the flatness of f around the (unique) limit point of (xk)k∈N

Year: 2013
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