Convex- and Monotone-Transformable Mathematical Programming Problems and a Proximal-Like Point Method |
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Authors: | J X Da Cruz Neto O P Ferreira L R Lucambio Pérez S Z Németh |
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Institution: | (1) DM, Universidade Federal do Piauí, Teresina, PI, 64049-500, BR;(2) IME, Universidade Federal de Goiás, Goiania, GO, 74001-970, BR;(3) Computer and Automation Institute, Hungarian Academy of Sciences, 1518 Budapest, P.O. Box 63, Hungary |
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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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