Optimization Toolbox

Nonlinear Least-Squares

An important special case for f(x) is the nonlinear least-squares problem

(4-12)

where is a vector-valued function with component i of equal to The basic method used to solve this problem is the same as in the general case described in Trust-Region Methods for Nonlinear Minimization. However, the structure of the nonlinear least-squares problem is exploited to enhance efficiency. In particular, an approximate Gauss-Newton direction, i.e., a solution s to

(4-13)

(where J is the Jacobian of ) is used to help define the two-dimensional subspace . Second derivatives of the component function are not used.

In each iteration the method of preconditioned conjugate gradients is used to approximately solve the normal equations, i.e.,

although the normal equations are not explicitly formed.

Box Constraints

Quadratic Programming