What Is Optimization Toolbox?

Least-Squares OptimizationThe linear predicted sum of squares is calculated as(3-20)and the term is obtained by cubicly interpolating the points and.Asteplengthparameter is also obtained from this interpolation,which is the estimated step to the minimum. If is greater than ,then is reduced, otherwise it is increased. The justification for this is thatthedifferencebetween and is a measure of the effectiveness ofthe Gauss-Newton method and the linearity of the problem. This determineswhether to use a direction approaching the steepest descent direction or theGauss-Newton direction.The formulas for the reduction and increase in , which have been developedthrough consideration of a large number of test problems, are shown in thefollowing figure.Figure 3-5:Updating λ kFollowing the update of , a solution of Equation 3-19 is used to obtain asearch direction, . A step length of unity is then taken in the direction, which is followed by a line search procedure similar to that discussedfor the unconstrained implementation. The line search procedure ensuresthatat each major iteration and the method is therefore adescent method.3-23