Newton and Quasi-Newton Methods for Normal Maps with Polyhedral Sets 1

@inproceedings{Han2003NewtonAQ,
  title={Newton and Quasi-Newton Methods for Normal Maps with Polyhedral Sets 1},
  author={Jeongheon Han and D.},
  year={2003}
}
We present a generalized Newton method and a quasiNewton method for solving H(x) := F(nc(x))+x-nc(x) = 0, when C is a polyhedral set. For both the Newton and quasi-Newton methods considered here, the subproblem to be solved is a linear system of equations per iteration. The other characteristics of the quasi-Newton method include: (i) a g-superlinear convergence theorem is established without assuming the existence of H' at a solution x* of H(x) = 0; (ii) only one approximate matrix is needed… CONTINUE READING

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