SENSOP: A derivative-free solver for nonlinear least squares with sensitivity scaling

Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

A Derivative-Free Algorithm for Least-Squares Minimization

We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are designed to take advantage of the problem structure by building polynomial interpolation models for each function in the least-squares minimization. Under suitable conditions, global convergence of the algorithm is established within a trust region framework. Promisi...

Sensitivity shaping with degree constraint by nonlinear least-squares optimization

This paper presents a new approach to shaping of the frequency response of the sensitivity function. A sensitivity shaping problem is formulated as an approximation problem relative to a desired frequency response and with respect to a function in a class of sensitivity functions with a degree bound. It is reduced to a finite dimensional constrained nonlinear least-squares optimization problem....

Nonlinear Least-squares Estimation

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Subspace Least Squares Multidimensional Scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of p...