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We apply methods of proof mining to obtain uniform quantitative bounds on thestrong convergence of the proximal point algorithm for finding minimizers ofconvex, lower semicontinuous proper functions in CAT(0) spaces. Thus, foruniformly convex functions we compute rates of convergence, while, for totallybounded CAT(0) spaces we apply methods introduced by Kohlenbach, the firstauthor and Nicolae to compute rates of metastability.

Effective strong convergence of the proximal point algorithm in CAT(0) spaces