The proximal point algorithm in metric spaces
- First Online:
- Cite this article as:
- Bačák, M. Isr. J. Math. (2013) 194: 689. doi:10.1007/s11856-012-0091-3
- 424 Downloads
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.