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IE417: Nonlinear Programming: Lecture 7
Jeff Linderoth
Department of Industrial and Systems Engineering
Lehigh University
7th February 2006
Jeff Linderoth
IE417:Lecture 7
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Today’s Outline
Review
Trust Regions
Jeff Linderoth
IE417:Lecture 7
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Stuff We Learned Last Time
A Horrible Proof of Kantorovich Inequality
Rate of Convergence: Newton’s Method
Assume we take Newton steps: If
∇
2
f
(
x
)
exists and is Lipschitz
continuous around the optimal solution
x
*
(at which the second
order sufficient conditions hold), then
1
If
x
0
is “sufficiently close” to
x
*
, then
{
x
k
} →
x
*
2
{
x
k
}
converges Qquadratically to
x
*
3
{ ∇
f
(
x
k
)
} →
0
at a Qquadratic rate.
Jeff Linderoth
IE417:Lecture 7
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Fun With Regular Expressions
What problems can you solve?
for i in $MASTSIF/*.SIF; do grep l ".*[QSO]UR2.*0$" $i; done
There are 157 problems in all!
Jeff Linderoth
IE417:Lecture 7
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 Spring '08
 Linderoth
 Optimization, Systems Engineering, Continuous function, Regular expression, Jeff Linderoth

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