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arXiv · 1503.02757

Projection onto simplicial cones by Picard's method

Jorge Barrios·Orizon P. Ferreira·Sándor Z. Németh
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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.

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Jorge Barrios, Orizon P. Ferreira, Sándor Z. Németh. 2015-03-10. Projection onto simplicial cones by Picard's method. https://arxiv.org/abs/1503.02757

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