Algorithms for solving nonlinear dynamic decision models

Nonlinearity, ComputationaL Complexity and Macroeconomic Modelling

“…So as m increases, the speed of convergence falls to that of linear first order iterations and the Newton method's advantage has been lost. An intermediate position is occupied by Becker and Rustem's (1993) N-SCE method which re-evaluates only parts of F and then only when it improves the rate of convergence. The same results must therefore apply, although the fall to linear convergence rates will of course be a little slower.…”

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“…The approximation to Jacobian ∇F µ (ζ ) can be either computed block by block, or using variations of BFGS method [2,3,6]. The special structure of ∇F µ (ζ ) can be exploited in a similar way as in [1].…”

“…It is desirable that a quasi-Newton algorithm also satisfies such a constraint. If it does not, then the Jacobian approximation is made more accurate by evaluating selected columns of ∇F µ (see [2]). One way of detecting the violation of assumption 3 is the failure of the merit function (12) to return a sufficiently large positive α k .…”