Abstract.
Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12--16], we study the set of their singularities and for a particularclass of manifolds develop an extragradient-type algorithm convergent to singularities of such vector fields. In particular, our method can be used forsolving nonlinear constrained optimization problems in Euclidean space, with a convex objective function and the constraint set a constant curvature Hadamard manifold. Our paper shows how tools of convex analysis on Riemannian manifolds can be used to solve some nonconvex constrained problem in a Euclidean space.
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O.P. Ferreira- was supported in part by CAPES, FUNAPE (UFG) and (CNPq).
S.Z. Németh- was supported in part by grant No.T029572 of the National Research Foundation of Hungary.
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Ferreira, O.P., Pérez, L.R.L. & Németh, S.Z. Singularities of Monotone Vector Fields and an Extragradient-type Algorithm. J Glob Optim 31, 133–151 (2005). https://doi.org/10.1007/s10898-003-3780-y
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DOI: https://doi.org/10.1007/s10898-003-3780-y