What Is Optimization Toolbox?

3 Standard Algorithmswhereis the n-by-n JacobianNewton’s method can run into difficulties. may be singular, and so theNewton step is not even defined. Also, the exact Newton step may beexpensive to compute. In addition, Newton’s method may not converge if thestarting point is far from the solution.Using trust-region techniques (introduced in “Trust-Region Methods forNonlinear Minimization” on page 4-3) improves robustness when startingfar from the solution and handles the case when is singular. To use atrust-region strategy, a merit function is needed to decide if is better orworse than . A possible choice isBut a minimum of is not necessarily a root of .The Newton stepis a root of3-26