A modified nearly exact method for solving low-rank trust region subproblem

In this paper, we first discuss how the nearly exact (NE) method proposed by More and Sorensen [14] for solving trust region (TR) subproblems can be modified to solve large-scale "low-rank" TR subproblems efficiently. Our modified algorithm completely avoids computation of Cholesky factori...

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Bibliographic Details
Published in:	Mathematical programming 2007-03, Vol.109 (2-3), p.385-411
Main Authors:	ZHAOSONG LU, MONTEIRO, Renato D. C
Format:	Article
Language:	eng
Subjects:	Algorithms Applied sciences Approximation Comparative studies Eigen values Exact sciences and technology Mathematical programming Matrix Methods Operational research and scientific management Operational research. Management science Optimization
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Summary:	In this paper, we first discuss how the nearly exact (NE) method proposed by More and Sorensen [14] for solving trust region (TR) subproblems can be modified to solve large-scale "low-rank" TR subproblems efficiently. Our modified algorithm completely avoids computation of Cholesky factorizations by instead relying primarily on the Sherman-Morrison-Woodbury formula for computing inverses of "diagonal plus low-rank" type matrices. We also implement a specific version of the modified log-barrier (MLB) algorithm proposed by Polyak [17] where the generated log-barrier subproblems are solved by a trust region method. The corresponding direction finding TR subproblems are of the low-rank type and are then solved by our modified NE method. We finally discuss the computational results of our implementation of the MLB method and its comparison with a version of LANCELOT [5] based on a collection extracted from CUTEr [12] of nonlinear programming problems with simple bound constraints. [PUBLICATION ABSTRACT]
ISSN:	0025-5610 1436-4646