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Value of opt[4] | Update Method |
1 | Automatic restart method of Powell (1977) and Beale (1972). |
This is the default. | |
2 | Fletcher-Reeves update (Fletcher 1987) |
3 | Polak-Ribiere update (Fletcher 1987) |
4 | Conjugate-descent update of Fletcher (1987) |
The NLPCG subroutine is useful for optimization problems with large n. For the unconstrained or boundary constrained case, the NLPCG method needs only order n bytes of working memory, whereas the other optimization methods require order n^{2} bytes of working memory. During n successive iterations, uninterrupted by restarts or changes in the working set, the conjugate gradient algorithm computes a cycle of n conjugate search directions. In each iteration, a line search is done along the search direction to find an approximate optimum of the objective function. The default line-search method uses quadratic interpolation and cubic extrapolation to obtain a step size that satisfies the Goldstein conditions. One of the Goldstein conditions can be violated if the feasible region defines an upper limit for the step size. You can specify other line-search algorithms with the fifth element of the opt argument.
For an example of the NLPCG subroutine, see "Constrained Betts Function" .
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