An interval method for bounding level sets of parameter estimation problems
The author examines the parameter estimation problem with objective function of sum-of-squares type: \(\min_{x\in X}f(x)=\sum^{m}_{i=1}(f_ i-f(i,x))^ 2\) where \(f_ i\) and f(i,x), \(i=1,2,...,m\) scalar functions of one and \(m+1\) arguments, respectively, and \(X=\{x\in {\mathbb{R}}^ n:\) \(a_ i\leq x_ i\leq b_ i\); \(a_ i,b_ i\in {\mathbb{R}}\), \(i=1,2,...,n\}\). The paper presents an algorithm that determines a bounding box by means of inclusion functions of the objective function and its gradient. The rate of convergence is studied, and cases when it is linear, superlinear or higher are shown. Examples examined prove that this algorithm sometimes can be used for nonlinear functions of more general form (not only those of least-squares form).
scientific article; zbMATH DE number 4088893