systems of equations – Optimization Online

New quasi-Newton method for solving systems of nonlinear equations

Published: 2017/06/22

Nonlinear Optimization, Nonlinear Systems and Least-Squares adjoint broyden methods, nonlinear equations, numerical algorithms, numerical experiments, systems of equations, trust-region methods, uasi-newton methods

In this report, we propose the new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but it is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires $O(n^2)$ … Read more

Global Optimization of Non-Linear Systems of Equations by Simulating the Flight of a Projectile in the Conformational Space

Published: 2008/10/20

Nicholas Harkiolakis

Nonlinear Optimization, Optimization Software and Modeling Systems, Stochastic Approaches flight, global, optimization, projectile, simulation, systems of equations

A new heuristic optimization algorithm is presented based on an analogy with the physical phenomenon of a projectile launched in a conformational space under the influence of a gravitational force. Its implementation simplicity and the option to enhance it with local search methods make it ideal for the optimization of non-linear systems of equations. The … Read more