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The Trust Region



Each iteration of LANCELOT involves finding an approximation to the optimium value of a suitable quadratic model  of the merit function within a suitably shaped region surrounding the current iterate. This region is known as the trust region. The user may choose between a ``box''  shaped, infinity norm region, which is specified by the keyword INFINITY-NORM-TRUST-REGION-USED and a ``spherical'' shaped region, which arises when the TWO-NORM-TRUST-REGION-USED keyword is used. The default is for

to be specified.