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MiS Preprint

Proximal Point Algorithm in Metric Spaces

Miroslav Bačák


The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of non-positive curvature. We prove that the sequence generated by the proximal point algorithm weakly converges to a minimizer, and also discuss a related question: convergence of the gradient flow.

Dec 9, 2011
Dec 9, 2011
proximal point algorithm, gradient flow semigroup, Nonpositive curvature

Related publications

2013 Repository Open Access
Miroslav Bačák

The proximal point algorithm in metric spaces

In: Israel journal of mathematics, 194 (2013) 2, pp. 689-701