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Review and Catchup
Nonlinear Programming
IE426: Optimization Models and Applications:
Lecture 21
Jeﬀ Linderoth
Department of Industrial and Systems Engineering
Lehigh University
November 21, 2006
Jeﬀ Linderoth
IE426:Lecture 21
Review and Catchup
Nonlinear Programming
Stochastic Programming
Review
Quiz #2
HW #4
Questions?
No Class
on 11/30
Homework Due 11/30 – In my mailbox by close of business!
TV People – Please have proctor verify that you turned in the
homework by 11/30.
You will need to know a little about nonlinear programming,
AMPL, and NEOS, so we’ll do that today.
Jeﬀ Linderoth
IE426:Lecture 21
Review and Catchup
Nonlinear Programming
Stochastic Programming
Final Discussion
Final is on 12/7 from 2:45PM–5:45PM
Location:
410 Packard Lab
TV People – You can take it
anytime
on 12/7
Contact me if you cannot take it from 2:45–5:45 on 12/7.
You will take it in the morning of 12/7
Jeﬀ Linderoth
IE426:Lecture 21
Review and Catchup
Nonlinear Programming
Stochastic Programming
Stochastic Programming Review
For stochastic programming, you will need to know how to do
the following:
1
Create the “supermodel”: The full stochastic model to
optimize the expected value of the decisions
2
Compute Value of Stochastic Solution
3
Compute the Expected Value of Perfect Information
Jeﬀ Linderoth
IE426:Lecture 21
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View Full DocumentReview and Catchup
Nonlinear Programming
Stochastic Programming
VSS and EVPI: Deﬁnitions
Let
S
: Set of scenarios
Let
s
: Be the
average
scenario. A scenario in which each
element is the average over all the elements in
S
Be sure to weight the average by the
probability
of each
scenario
Let
SP
: Stochastic program
Let
LP
(ˆ
s
)
: Linear program that gives optimal (ﬁrst and
second stage) actions if scenario
ˆ
s
happens
Let
LP
(ˆ
x,s
)
: Linear program that gives optimal (second
stage) actions if scenario
ˆ
s
happens,
and
ﬁrst stage decisions
ˆ
x
are taken
Jeﬀ Linderoth
IE426:Lecture 21
Review and Catchup
Nonlinear Programming
Stochastic Programming
More Deﬁnitions
Let
v
(
·
)
: Be the
value
of the corresponding problem.
Let
x
(
·
)
: Be an
optimal solution
to the named problem.
v
(
SP
)
: Value of optimal solution to SP
v
(
LP
(
s
))
: Optimal solution value of
LP
(
s
)
x
(
LP
(
s
))
: Optimal solution to
LP
(
s
)
Jeﬀ Linderoth
IE426:Lecture 21
Review and Catchup
Nonlinear Programming
Stochastic Programming
VSS
These deﬁnitions assume
maximization
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 Spring '08
 Linderoth
 Optimization, Systems Engineering

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