2 %> Algorithm 12.1: Calculation of the intersection with the trust region. Implementation of algorithm 12.1 of \cite Bier15-book
4 %> @note Tested with \ref runIntersectionTrustRegion.m
5 %> @note Called by \ref
dogleg 7 %> @author Michel Bierlaire
8 %> @date Sat Mar 21 15:37:52 2015
12 %> Calculate the step along a direction that is on the border of the trust region centered at 0
14 %> @param x a point within the trust region , that is such that \f$ \|x\| \leq \Delta \|\f$.
15 %> @param d the direction
16 %> @param delta the radius \f$ \Delta\f$ of the trust region
17 %> @
return lambda The step \f$ \lambda\f$ such that \f$ \|x + \lambda d\|_2 = \Delta\f$.
21 c = x
' * x - delta * delta ; 22 d = b * b - 4.0 * a * c ; 23 lambda = (- b + sqrt(d) ) / (2.0 * a) ; function intersectionTrustRegion(in x, in d, in delta)
Calculate the step along a direction that is on the border of the trust region centered at 0...
function dogleg(in g, in H, in delta)
Given a current iterate , consider the trust region subproblem subject to Apply the Dogleg method t...