Variable projection for nonlinear least squares problems

Superlinearly convergent exact penalty projected structured Hessian updating schemes for constrained nonlinear least squares: asymptotic analysis

We present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of N...

An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems

This paper considers an efficient iterative approach to solve separable nonlinear least squares problems that arise in large scale inverse problems. A variable projection GaussNewton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative Lanczos hybrid scheme. Regularization parameters are chosen automatically using a weighted...

Separable Nonlinear Least Squares: the Variable Projection Method and its Applications

Radial function collocation solution of partial differential equations in irregular domains

We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domain...

Estimation of atmospheric PSF parameters for hyperspectral imaging

We present an iterative approach to solve separable nonlinear least squares problems arising in the estimation of wavelength-dependent point spread function (PSF) parameters for hyperspectral imaging. A variable projection Gauss-Newton method is used to solve the nonlinear least squares problem. An analysis shows that the Jacobian can be potentially very ill-conditioned. To deal with this ill-c...