A New Matrix { Free Algorithm for the Large { ScaleTrust { Region SubproblemSandra
نویسندگان
چکیده
The trust{region subproblem arises frequently in linear algebra and optimization applications. Recently, matrix{free methods have been introduced to solve large{ scale trust{region subproblems. These methods only require a matrix{vector product and do not rely on matrix factorizations 4, 7]. These approaches recast the trust{ region subproblem in terms of a parameterized eigenvalue problem and then adjust the parameter to nd the optimal solution from the eigenvector corresponding to the smallest eigenvalue of the parameterized eigenvalue problem. This paper presents a new matrix{free algorithm for the large{scale trust{region subproblem. The new algorithm improves upon the previous algorithms by introducing a uniied iteration that naturally includes the so called hard case. The new iteration is shown to be superlinearly convergent in all cases. Computational results are presented to illustrate convergence properties and robustness of the method.
منابع مشابه
A New Matrix { Free Algorithm for the Large { ScaleTrust { Region
We present a matrix{free algorithm for the large{scale trust{region sub-problem. 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 nd the optimal solution of the trust{region subproblem from the eigenvectors associated ...
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