null space methods – Optimization Online

A basis-free null space method for solving generalized saddle point problems

Published: 2015/09/08, Updated: 2015/11/03

Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs analytical solutions, conditioning, direct methods, indefinite linear systems, matrix inversion, null space methods, preconditioning, saddle point problem

Using an augmented Lagrangian matrix approach, we analytically solve in this paper a broad class of linear systems that includes symmetric and nonsymmetric problems in saddle point form. To this end, some mild assumptions are made and a preconditioning is specially designed to improve the sensitivity of the systems before the calculation of their solutions. … Read more

A Null Space Method for Solving System of Equations

Published: 2003/02/22, Updated: 2003/02/26

Nie Pu-yan

Nonlinear Optimization equality constraints, global convergenc, nonlinear programming, nonlinear system of equations, null space methods

We transform the system of nonlinear equations into a nonlinear programming problem, which is solved by null space algorithms. We do not use standard least square approach. We divide the equations into two groups. One group contains the equations that are treated as equality constraints. The square of other equations is regarded as objective function. … Read more