Solve the following NLP: { <mtable rowspacing="4pt" columnspacing="1em"> <m

Desirae Washington 2022-07-06 Answered
Solve the following NLP:
{ min 3 x + y z 2 s . t g ( x , y , z ) = x + y + z 0 h ( x , y , z ) = x + 2 y + z 2 z = 0

My attempt
Using kkt conditions, we have 2 possibles situations:
1) If g < 0: f + λ h = 0 , h = 0
{ 3 λ = 0 3 y 2 + 1 + 2 λ = 0 2 λ z = 0 x + 2 y + z 2 = 0
From first and second, we see it is impossible
**2)** g = 0: f + λ h + μ g = 0 , μ 0
{ 3 λ + μ = 0 3 y 2 + 1 + 2 λ + μ = 0 2 λ z + μ = 0 x + 2 y + z 2 = 0 x + y + z = 0
I couldnt solve this last one. Any idea? I've tried to put y,z im function of μ and use the last 2 eq., but didnt work (it became complicated).
Thanks in advance!
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Answers (1)

Alexis Fields
Answered 2022-07-07 Author has 14 answers
x = 2 y + z 2 3 y + z + z 2 0 y z 2 + z 3 , 3 x + y z 2 = 6 y 3 z 2 + y z 2 = 5 y 4 z 2 5 ( z 2 + z ) 3 4 z 2 = 7 z 2 5 z 3
it seems no min when z

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