1D Newton's Method
Figure 1. Plot of a). quartic
polynomial with iterative solutionm points and b). convergence curve.
Objective:
Find global minimum of non-linear function using 1D version
of Newton's method.
Introduction:
Iterative 1D Newton method for finding minimizer
of quartic polynomial function.
Procedure:
- Load and execute program Newt1a.m.
Adjust quartic constants and explain change in convergence rate.
-
Add a step length term so you don't go uphill. Reduce alpha
from 1 to smaller positive values until you dont go uphill.
-
Add a constraint penalty function lambda(x-.3)^2 to misfit function
so you quickly get near actual solution. Decrease lamba
as iterations proceed.
- Start with a large positive value of lambda and gradually reduce it
zero as iterations proceed. Does this help increase convergence rate?
Why?