Matrix-free method for nonlinear least squares minimization

What is it about?

We present a matrix-free algorithm that satisfies the descent direction condition for solving nonlinear least squares problem.

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Why is it important?

We have proposed a structured diagonal Hessian approximation algorithm for solving nonlinear least-squares problems. The presented algorithm is a Jacobian-free strategy, requiring neither to form nor to store the Jacobian matrix. Instead, it requires only a loop-free subroutine for computing the product of the Jacobian transpose by a vector. This is an advantage, especially for very large-scale and structures problems. In addition, our proposed method is suitable for both zero and non-zero residual problems.

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