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Dedicated to M. J. D. Powell, master of convergence analysis for nonlinear optimization, on the occasion of his 70th birthday. Shor's r-algorithm is an iterative method for unconstrained optimization, designed for minimizing nonsmooth functions, for which its reported success has been considerable. Although some limited convergence results are known, nothing seems to be known about the algorithm's rate of convergence, even in the smooth case. We study how the method behaves on convexdoi:10.1093/imanum/drn008 fatcat:e32axyq6ozc2pe6wjqkgp5i4si