May 2015
Intermediate to advanced
466 pages
10h 33m
English
Content preview from Optimization
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174 Optimization: Algorithms and Applications
Let us check for the optimality condition
−∇f(x) = μ
1
∇g
1
(x) + μ
2
∇g
2
(x)
for some μ
1
and μ
2
which are ≥0.
It can be shown that at point A
0 5
0 875
0 4218
1 5
1
0 4531
2 5
1
.
.
.
.
.
.
≈
−
+
Thus, for positive value of multipliers (μ
1
= 0.4218 and μ
2
= 0.4513), the
negative of the gradient of the objective function can be expressed as a
linear combination of the gradient of the constraints. KKT conditions are
satised at point A. Thus, point A is a candidate for the minimum of the
function. Let us check the second-order condition as
∇ =
− +
=
2
1 2
2 2 0
0 2
0 25 0
0 2
L
( )
.
µ µ
As this matr ...
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