Solve Linear Programming Homework: Global Min @ (0,0)

[Freydulf]

Homework Statement

Solve:

http://www.rinconmatematico.com/latexrender/pictures/0399b7f0b179dcbf396e72f315e6d219.png

Homework Equations

The Attempt at a Solution

http://www.rinconmatematico.com/latexrender/pictures/5a8e45f50b7d55e4c8ab2c5ce3b7d554.png
http://www.rinconmatematico.com/latexrender/pictures/dfd7077296a65ae4d3a0b0f409ef0118.png

http://www.rinconmatematico.com/latexrender/pictures/be995f308f56dfd08931544079d643eb.png

http://www.rinconmatematico.com/latexrender/pictures/76941dbf58eb6b6a6a5abb3f76c2326c.png
http://www.rinconmatematico.com/latexrender/pictures/8b328666878b3c586f55614fc7162373.png

http://www.rinconmatematico.com/latexrender/pictures/3846f3e2531e839b39ea7f5626b7c0ef.png

Positive-semidefinite, it has a global minimum at (0,0).


Well, that's what I've done til now. I'm not sure whether it's right, can someone give me a hand? :)

 

[LeBrad]

Can you explain what you're trying to do? It's hard to help without understanding your approach.

http://www.rinconmatematico.com/latexrender/pictures/be995f308f56dfd08931544079d643eb.png


Positive-semidefinite, it has a global minimum at (0,0).

I'm guessing you're trying to show that the function has a positive semi-definite Hessian, which implies convexity, which implies global minimum. However, what you have there is certainly not positive semidefinite.

http://www.rinconmatematico.com/latexrender/pictures/76941dbf58eb6b6a6a5abb3f76c2326c.png
http://www.rinconmatematico.com/latexrender/pictures/8b328666878b3c586f55614fc7162373.png

http://www.rinconmatematico.com/latexrender/pictures/3846f3e2531e839b39ea7f5626b7c0ef.png

Do you really believe this? You are essentially saying that both the function $z^3$ and the function $-z^3$ are both non-negative for all z.

Assuming you're trying to look at the Hessian, try differentiating again. It contains SECOND derivatives.

 

[HallsofIvy]

This is certainly NOT "linear programming". Your equations are not linear.