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:

  1. Load and execute program Newt1a.m. Adjust quartic constants and explain change in convergence rate.
  2. Add a step length term so you don't go uphill. Reduce alpha from 1 to smaller positive values until you dont go uphill.
  3. Add a constraint penalty function lambda(x-.3)^2 to misfit function so you quickly get near actual solution. Decrease lamba as iterations proceed.
  4. Start with a large positive value of lambda and gradually reduce it zero as iterations proceed. Does this help increase convergence rate? Why?