A trust-region method approximately minimizes a local model inside a bounded neighborhood, then tests the step using the trust-region acceptance ratio. Poor agreement rejects the trial and shrinks the radius; sufficient agreement accepts it; very good agreement may justify expanding the radius. A fraction of Cauchy decrease gives a quantitative minimum quality for approximate subproblem solves. The radius is an adaptive measure of the model's usable range, rather than a prescribed sequence tending to zero.
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