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arXiv · 1206.7074

The proximal point algorithm in metric spaces

Miroslav Bacak
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Abstract

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 nonpositive 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.

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Miroslav Bacak. 2012-06-29. The proximal point algorithm in metric spaces. https://arxiv.org/abs/1206.7074

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