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Assessing a search direction within a truncated Newton method. (English) Zbl 0706.90073
Truncated Newton methods for nonlinear optimization compute a search direction by approximately solving the Newton equations, typically via the conjugate gradient algorithm. The search direction is usually assessed using the norm of the residual. This short paper shows that the norm of the residual can be an arbitrarily poor predictor of a good search direction, and the results of the paper suggest that the search direction should be assessed in terms of the quadratic function instead of the norm of the residual.
Reviewer: S.Wang

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
90-08 Computational methods for problems pertaining to operations research and mathematical programming
Full Text: DOI
[1] Dembo, R.S.; Steihaug, T., Truncated-Newton algorithms for large-scale unconstrained optimization, Math. programming, 26, 190-212, (1983) · Zbl 0523.90078
[2] Golub, G.H.; van Loan, C., Matrix computations, (1983), The Johns Hopkins University Press Baltimore, MD · Zbl 0559.65011
[3] Nash, S.G., Truncated-Newton methods, () · Zbl 0592.65038
[4] Nash, S.G., Truncated-Newton methods for large-scale function minimization, (), 91-100
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