Abstract
The problem of finding the singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will also be shown how tools of convex analysis on Riemannian manifolds can solve non-convex constrained problems in Euclidean spaces. To illustrate this remarkable fact examples will be given.
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Da Cruz Neto, J.X., Ferreira, O.P., Pérez, L.R.L. et al. Convex- and Monotone-Transformable Mathematical Programming Problems and a Proximal-Like Point Method. J Glob Optim 35, 53–69 (2006). https://doi.org/10.1007/s10898-005-6741-9
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DOI: https://doi.org/10.1007/s10898-005-6741-9