Projection onto simplicial cones by Picard's method
Optimization and Control
2015-03-11 v1
Abstract
By using Moreau's decomposition theorem for projecting onto cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations. It is shown that Picard's method applied to the system of equations associated to the problem of projecting onto a simplicial cone generates a sequence that converges linearly to the solution of the system. Numerical experiments are presented making the comparison between Picard's and semi-smooth Newton's methods to solve the nonsmooth system associated with the problem of projecting a point onto a simplicial cone.
Keywords
Cite
@article{arxiv.1503.02757,
title = {Projection onto simplicial cones by Picard's method},
author = {Jorge Barrios and Orizon P. Ferreira and Sándor Z. Németh},
journal= {arXiv preprint arXiv:1503.02757},
year = {2015}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:1404.2427