2014/04/09 by Ferreira, O. P., Németh, S. Z.
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Primary 90C33 #Secondary 15A48
paper · doi:10.48550/arxiv.1404.2427
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 a semi-smooth Newton method applied to the system of equations associated to the problem of projecting onto a simplicial cone is always well defined, and the generated sequence is bounded for any starting point and under a somewhat restrictive assumption it is finite. Besides, under a mild assumption on the simplicial cone, the generated sequence converges linearly to the solution of the associated system of equations.