need help in Kuhn tucker nonlinear analysis

Status
Not open for further replies.
S

soul_

Newbie level 4
Joined
Aug 27, 2010
Messages
6
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,315
Find the Max value of F(U)=u1^2+u2^2+u3^2 (and the values of ui to produce the maximum of F) subject to
u1-u2+u3=1
u1^2+u2^2<=2
u2^2+u3^2<=4

[If this is not clear please find the atttached document]
 

Attachments

  • Find the Max value of F.doc
    22 KB · Views: 126

F(U) = u1^2+u2^2+u3^2 is the distance^2 to origin.

u1-u2+u3=1
u1^2+u2^2<=2
u2^2+u3^2<=4

Are the intersection of 2 ellipses (a 4th deg equation)==> the real solution more distant to the origin will be the maximum of F(U)

WolframAlpha said http://www.wolframalpha.com/input/?i=x-y%2Bz%3D1+and+x^2%2By^2%3D2+and+y^2%2Bz^2%3D4++

--> two real solutions:
U1 = [ -1.35731, -0.397133, 1.96017 ]
U2 = [ 0.675347, 1.24254, 1.56719 ]

but F(U1) > F(U2) then the solution is

U = [ -1.35731, -0.397133, 1.96017 ]
F(U) ~ 5.8422
 

Status
Not open for further replies.

Similar threads

Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…