Scalable subspace methods for derivative-free nonlinear least-squares optimization

Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

Sequential Penalty Derivative-Free Methods for Nonlinear Constrained Optimization

We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor approximated explicitly. Hence, every minimization procedure must use only a suitable sampling of the problem functions. These problems ...

Inner-Iteration Krylov Subspace Methods for Least Squares Problems

Stationary inner iterations in combination with Krylov subspace methods are proposed for least squares problems. The inner iterations are efficient in terms of computational work and memory, and serve as powerful preconditioners also for ill-conditioned and rank-deficient least squares problems. Theoretical justifications for using the inner iterations as preconditioners are presented. Numerica...

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...

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...