Homework 9 Foundations of Computational Math 1 Fall
2010
There will be no specific program assigned for optimization.
As mentioned in class, it
is a good idea to implement the basic methods explore their behavior and compare it to
the results of the convergence analysis in the notes, homework and textbook. For systems
and optimization, Newton’s method is recommended for consideration.
This can be used
with step
α
k
= 1 as in the exercise on Newton’s method for scalar optimization below or
with a simple line search as mentioned in the notes.
For unconstrained optimization, the
BFGS method is the standard QuasiNewton method although care must to avoid directions
of negative curvature and to select
α
k
.
However, some simple experiments can give you
the flavor of its performance and problems. Important theoretical and practical details on
Newton, QuasiNewton and other methods for unconstrained optimization are discussed in
the numerical optimization courses.
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 Spring '11
 Gallivan
 Multivariable Calculus, General Relativity, hessian matrix, Newton's method in optimization

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