How can I derive my Lagrange Function (handwritten) into the form from the other screenshot?    Parameter: c = [-5, -3] A = [[2, 2], [2, -4], [-2, 1], [0, -1], [0, 1]] b = [33, 8, 5, -1, 8]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How can I derive my Lagrange Function (handwritten) into the form from the other screenshot? 

 

Parameter: c = [-5, -3] A = [[2, 2], [2, -4], [-2, 1], [0, -1], [0, 1]] b = [33, 8, 5, -1, 8]

2(x, 2) =
бlix, 2)
бх
5x - 3x2 + 2 (2х, +2x2-33) +
х2 (2x,-их2-8)
X4
(-X₂ + 1)
=
5x
+
8+
2з 1-2X, + Хz2-5)
25
(72:8)
2 дит.24]
(-332-872 - 523 + ди
8же
ихл
523 ]
[
8xg)
(−5+22₁ +22₂ -273)
хе 1-3+221-их 2+23-24)
-8ks]
33]
2.72.
из
хи
=0
Transcribed Image Text:2(x, 2) = бlix, 2) бх 5x - 3x2 + 2 (2х, +2x2-33) + х2 (2x,-их2-8) X4 (-X₂ + 1) = 5x + 8+ 2з 1-2X, + Хz2-5) 25 (72:8) 2 дит.24] (-332-872 - 523 + ди 8же ихл 523 ] [ 8xg) (−5+22₁ +22₂ -273) хе 1-3+221-их 2+23-24) -8ks] 33] 2.72. из хи =0
Example: Linear Programming
Therefore, the dual Lagrangian is D(A) = -A¹b. Recall we would like
to maximize (X). In addition to the constraint due to the derivative of
L(x, A) being zero, we also have the fact that X > 0, resulting in the
following dual optimization problem
80 von 84
- bTx
max
XER™
subject to c+A¹A=0
A > 0.
(7.43)
Transcribed Image Text:Example: Linear Programming Therefore, the dual Lagrangian is D(A) = -A¹b. Recall we would like to maximize (X). In addition to the constraint due to the derivative of L(x, A) being zero, we also have the fact that X > 0, resulting in the following dual optimization problem 80 von 84 - bTx max XER™ subject to c+A¹A=0 A > 0. (7.43)
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