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Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds

Erik A. Papa QuirozP. Roberto Oliveira — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...

Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds

Erik A. Papa QuirozP. Roberto Oliveira — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...

Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds

Erik A. Papa QuirozP. Roberto Oliveira — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...

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