This paper discusses the classical problem of least-square optimization on a finite dimensional space. Instead of using the classical techniques, such as the Levenberg-Marquandt or Gauss-Newton method, to find the minimum, the author presents a new method that uses the interval arithmetic and inclusion functions (set-valued functions) to determine bounding boxes (n-dimensional parallelipipeds) for level sets. This method is particularly suitable for the sensitivity analysis of saddle points as opposed to the procedure that determines confidence intervals by using local information provided by the Hessian matrix evaluated at the saddle points.

The paper describes the new procedure, presents an algorithm, discusses its convergence, and concludes with an example.