by Ra A. Santos, Marielba Rojas, Marielba Rojas, Sandra A. Santos, Danny C. Sorensen, Danny C. Sorensen
SIAM Journal on Optimization
ftp://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR99795.ps.gz
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Abstract:
We present a matrix--free algorithm for the large--scale trust--region subproblem. Our algorithm relies on matrix--vector products only and does not require matrix factorizations. We recast the trust--region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter. We then find the optimal solution of the trust--region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter. The new algorithm uses a different interpolating scheme than existent methods and introduces a unified iteration that naturally includes the so-called hard case. We show that the new iteration is well defined and convergent at a superlinear rate. We present computational results to illustrate convergence
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