Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares

Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization

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...

Gradient methods and conic least-squares problems

This paper presents two reformulations of the dual of the constrained least squares problem over convex cones. In addition, it extends Nesterov’s excessive gap method 1 [21] to more general problems. The conic least squares problem is then solved by applying the resulting modified method, or Nesterov’s smooth method [22], or Nesterov’s excessive gap method 2 [21], to the dual reformulations. Nu...

Parallel Tensor Methods for Nonlinear Equations and Nonlinear Least Squares

We describe the design and computational performance of parallel row-oriented tensor algorithms for the solution of dense systems of nonlinear equations and nonlinear least squares problems on a distributed-memory MIMD multiprocessor. Tensor methods are general purpose methods that base each iteration upon a quadratic model of the nonlinear function, rather than the standard linear model, where...

Least Squares Methods for System Identification of Structured Models

The purpose of system identification is to build mathematical models for dynamical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computationally efficient algorithms. For estimation of parametric models, the prediction error method (PEM) is a benchmark in the field. When the noise is Gaussian and...