Proximal point method for a special class of nonconvex functions on Hadamard manifolds
By G. C. Bento, Orizon Pereira Ferreira, P. Oliveira. 2008
135 citations recorded by the source corpus.
In this article, we present the proximal point method for finding minima of a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is established. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minima is obtained.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/53161784ccd6c91b5dca76961f767145e5b6b2a2
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In Computational Theory and Mathematics
In Geometry and Topology
In Numerical Analysis
Citations in the corpus
- The proximal point algorithm in metric spaces (2012, methodology): “In particular, the proximal point algorithm in the context of Riemannian manifold (of nonpositive sectional curvature) was studied in [6, 12, 20, 24].”
- Nash-type equilibria on Riemannian manifolds: a variational approach (2016, methodology): “Our examples are motivated by some applications from Bento, Ferreira and Oliveira [3], [4], Colao, López, Marino and Mart́ın-Márquez [13], and Li and Yao [26].”