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ACCELERATING THE LSTRS ALGORITHM
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DOI：10.1137/090764426.png)
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The LSTRS software for the efficient solution of the large-scale trust-region sub-problem was proposed in [M. Rojas, S. A. Santos, and D. C. Sorensen, ACM Trans. Math. Software, 34 (2008), article 11]. The LSTRS method is based on recasting the problem in terms of a parameter-dependent eigenvalue problem and adjusting the parameter iteratively. The essential work at each iteration is the solution of an eigenvalue problem for the smallest eigenvalue of a bordered Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Using the nonlinear Arnoldi method to solve the eigenvalue problems makes it possible to recycle most of the information from previous iterations which can substantially accelerate LSTRS.
Keyword:
constrained quadratic optimization
regularization
trust-region
ARPACK
nonlinear Arnoldi method
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