A two-phase-like proximal point algorithm in domains of positivity

This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting....

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 343; pp. 67 - 89
Main Authors:	Gregório, R.M., Oliveira, P.R., Alves, C.D.S.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15-02-2019
Subjects:	Compact Lie group Hadamard manifold Homogeneous domain of positivity Proximal point algorithm Weighted Lpcenter of mass 57S15 Homogeneous domain of positivity Compact Lie group 53C35 Hadamard manifold 65K10 53C25 Proximal point algorithm 43A07 Weighted Lpcenter of mass
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Summary:	This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted Lp (p=1,2) centers of mass are performed to demonstrate the practical feasibility of the method.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2018.09.054