nonlinear system of equations – Optimization Online

Spectral Residual Method for Nonlinear Equations on Riemannian Manifolds

Published: 2020/09/19, Updated: 2020/12/31

Nonlinear Systems and Least-Squares non-monotone line search, nonlinear system of equations, riemannian manifold, spectral residual method, tangent vector field

In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to the problem of finding a zero of a given tangent vector field on a Riemannian manifold. The generalized version of SANE uses, in a systematic way, the tangent vector field as a search direction and a continuous real–valued function that adapts this … 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