EAS6939 Homework #4 (Due: 3/22)
1. Consider the following design optimization problem:
22
1
2
1
11
3
3
2
1
Minimize
( )
4
4
Subject to
( )
0
( )
0
( )
(1
)
0
f
x
x
x
gx
g
x
x
x
x
x
x
(i)
Find the optimum point graphically
(ii)
Show that the optimum point does not satisfy KT condition. Explain
2. An engineering design problem is formulated as:
Minimize
1
2
1
2
( )
2
5
2
10
f
x
x
x
x
x
Subject to
the constraints
1
1
2
1
1
2
2
3
0
3
2
6
0
h
x
x
g
x
x
In all of the following questions, justify your answers.
(i)
Write KT necessary conditions
(ii)
How many cases are there to be considered? Identify those cases.
(iii)
Find the solution for the case where g
1
is active. Is this acceptable case?
(iv)
Regardless of the solution you obtained in (iii), suppose the Lagrange multiplier for
the constraint
h
1
= 0 is
1
= 2 and the Lagrange multiplier for the constraint
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This note was uploaded on 02/15/2012 for the course EAS 6939 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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