Levenberg Marquardt algorithm

From Glossary

Jump to: navigation, search

This is designed for solving nonlinear programs using the equation:

(\nabla^2 f(x) + p I)d = -\nabla f(x),

where LaTeX: \nabla^2 f(x) is the Hessian. For unconstrained optimization, the solution LaTeX: d serves as a direction vector for the iteration. This is also used in a trust region method. The parameter LaTeX: p is set to give a balance between Newton's method LaTeX: (p=0) and Cauchy's steepest descent LaTeX: (p >> 0). A low value of LaTeX: p helps get through difficult landscape curvature, and a high value yields some descent.

Personal tools