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

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 algo-rithm. 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 con-strained problems in Euclidean spaces. To illustrate this remarkable fact examples will be given. 1