A modified nearly exact method for solving low-rank trust region subproblem |
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Authors: | Zhaosong Lu Renato D C Monteiro |
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Institution: | (1) Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 156, CANADA;(2) School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA |
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Abstract: | In this paper, we first discuss how the nearly exact (NE) method proposed by Moré 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.
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Keywords: | Nearly exact method Trust region method Large-scale optimization Limited-memory BFGS method Sherman– Morrison– Woodbury formula |
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