View source for MLDO Problem 1 DOT formulation

[[MLDO_Problem_One#Original_Problem:_All_At_Once|back]]

== All At Once ==

=== DECLARATIONS ===

<pre>
NDV =  7   (# design variables)
NCON = 6   (# constraints)
</pre>

=== OBJECTIVE FUNCTION ===
<pre>
OBJ = X(1)*X(1)+X(2)*X(2)
</pre>
=== DESIGN CONSTRAINTS ===
<pre>
G(1)= (1.0/X(3)**2 + X(4)**2)/X(5)**2 - 1.0
G(2)= (X(5)**2 + 1.0/X(6)**2)/X(7)**2  - 1.0
G(3)= X(1)**2 - X(3)**2 - 1.0/X(4)**2 - X(5)**2
G(4)=-X(1)**2 + X(3)**2 + 1.0/X(4)**2 + X(5)**2
G(5)= X(2)**2 - X(5)**2 - X(6)**2 - X(7)**2
G(6)=-X(2)**2 + X(5)**2 + X(6)**2 + X(7)**2
</pre>

constraints X(i)=>0 , i=1,7 achieved by setting lb(i)=0.0

== Results ==

initial values: X(I)=1.0; LB(I)=0.0; UB(I)=25.0; I=1,7


{| border="1" cellpadding="3"
|-
| || x1 || x2 || x3 || x4 || x5 || x6 || x7||objective
|-
|Saber||2.15||2.06||1.32||0.76||1.07||1.00||1.47||
|- 
|DOT 1 || 2.17|| 2.06||1.28|| 0.72||1.06||1.04||1.43|| 8.95
|-
|DOT 2 || 2.15||2.07||1.32|| 0.76||1.07||1.00||1.46|| 8.93
|-
|DOT 3 || 2.15||2.07||1.32||0.76||1.07||1.00||1.47||8.93
|-
|CFSQP ||2.27||1.95||1.33||0.61||0.97||1.00||1.39|| 8.98
|-
|ATC_AL_1||2.25||2.00||1.33||0.66||1.00||1.05||1.38
|-
|}

where DOT i means DOT METHOD i

== Conclusions ==
DOT 2 and DOT 3 results are very close to that obtained by Saber.