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

Erik A. Papa Quiroz, P. Roberto Oliveira

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

14 Citas (Scopus)

Resumen

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 case, we prove the convergence of the iterations given by the method. Furthermore, under the assumptions that the sequence of proximal parameters is bounded and the function is continuous, we obtain the convergence to a generalized critical point. In particular, our work extends the applications of the proximal point methods for solving constrained minimization problems with nonconvex objective functions in Euclidean spaces when the objective function is convex or quasiconvex on the manifold.

Idioma originalInglés
Páginas (desde-hasta)483-500
Número de páginas18
PublicaciónESAIM - Control, Optimisation and Calculus of Variations
Volumen18
N.º2
DOI
EstadoPublicada - abr. 2012

Huella

Profundice en los temas de investigación de 'Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds'. En conjunto forman una huella única.

Citar esto