Dogleg Trust-Region Step

The dogleg method computes an approximate solution to the trust-region subproblem by restricting the search to a piecewise linear path. This path connects the origin, the Cauchy point (the minimizer along the steepest descent direction), and the unconstrained Newton point.

Experiment

Use the module controls to explore how the step choice changes with the trust radius and the current point.

1. Set Point x to 1, Point y to 1, and Trust radius to 2. Notice that the step chosen is exactly the Newton point since it fits inside the large trust region.
2. Change the Trust radius to 1. The Newton point is now outside the region. The Cauchy point is also slightly outside, so the step is scaled back along the steepest descent direction, landing on the Cauchy boundary.
3. Set Point x to 0 and Point y to 0. At this stationary point, the gradient is zero, so the step is exactly zero regardless of the trust radius.