Convex- and Monotone- Transformable Mathematical Programming Problems and a Proximal-Like Point Method

J. X. da Cruz Neto (jxaviermat.ufpi.br)
O. P. Ferreira (orizonmat.ufg.br)
L. R. Lucambio Perez (lrlpmat.ufg.br)
S. Z. Nemeth (snemethsztaki.hu)

Abstract: The problem of finding 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 be also 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.

Keywords: monotone vectors fields , Hadamard manifolds, proximal point algorithm

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 2: Global Optimization (Theory )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

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Entry Submitted: 08/20/2003
Entry Accepted: 08/20/2003
Entry Last Modified: 08/20/2003

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