@Article{Erway:2014:AMM,
  author =       "Jennifer B. Erway and Roummel F. Marcia",
  title =        "Algorithm 943: {MSS}: {MATLAB} Software for {L-BFGS} Trust-Region
                  Subproblems for Large-Scale Optimization",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       40,
  number =       4,
  year    =      2014,
  month   =      jun,
  pages =        "28:1--28:12",
  url =          "http://doi.acm.org/10.1145/2616588",
  accepted =     "12 November 2013",
  abstract =     "
                  A MATLAB implementation of the Mor\{'}e-Sorensen sequential
                  (MSS) method is presented. The MSS method computes
                  the minimizer of a quadratic function defined by
                  a limited-memory BFGS matrix subject to a two-norm
                  trust-region constraint. This solver is an adaptation of
                  the More-Sorensen direct method into an L-BFGS setting
                  for large-scale optimization. The MSS method makes use of
                  a recently proposed stable fast direct method for solving
                  large shifted BFGS systems of equations [Erway and
                  Marcia 2012; Erway et al. 2012] and is able to compute
                  solutions to any user-defined accuracy. This MATLAB
                  implementation is a matrix-free iterative method for
                  large-scale optimization. Numerical experiments on the
                  CUTEr [Bongartz et al. 1995; Gould et al. 2003]) suggest
                  that using the MSS method as a trust-region subproblem
                  solver can require significantly fewer function and
                  gradient evaluations needed by a trust-region method as
                  compared with the Steihaug-Toint method.",
}