Trust region is a term used in mathematical optimization to denote the subset of the region of the objective function to be optimized that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the trust region then the region is expanded; conversely, if the approximation is poor then the region is contracted. Trust region methods are also known as restricted step methods.
The fit is evaluated by comparing the ratio of expected improvement from the model approximation with the actual improvement observed in the objective function. Simple thresholding of the ratio is used as the criteria for expansion and contraction—a model function is "trusted" only in the region where it provides a reasonable approximation.
Trust region methods are in some sense dual to line search methods: trust region methods first choose a step size (the size of the trust region) and then a step direction while line search methods first choose a step direction and then a step size.
This class implements a simplified version of Chih-Jen Lin and Jorge Moré's TRON, a trust region Newton method for the solution of large bound-constrained optimization problems. This version was based upon liblinear's implementation.
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