Measurement inversion with a non-linear model
Inverse problems in heat diffusion . Construction and solution of the least squares problem

We have seen that, in the case of the linear model, the solution to the optimization problem is obtained simply by the relationship (8) and that the possibly ill-posed character derives from the characteristics of the information matrix S^T S.

In the case of a non-linear model, an additional difficulty arises in obtaining the minimum, which can become very tricky. This minimization is iterative, and the problem of convergence to the minimum arises.

In this section, we explain the general principles of descent methods and how to solve them. We explain the principle of first- and second-order methods, and discuss zero-order methods.

It is also...