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

• Freydulf
In summary: You need to identify what function you're trying to solve for, and then find the corresponding Hessian.
Freydulf

Homework Statement

Solve:

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

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? :)

Last edited by a moderator:
Can you explain what you're trying to do? It's hard to help without understanding your approach.

Freydulf said:
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.

Last edited by a moderator:
This is certainly NOT "linear programming". Your equations are not linear.

1. What is linear programming?

Linear programming is a mathematical method used to optimize a linear objective function, subject to linear equality and inequality constraints. It is commonly used in operations research, economics, and engineering to solve problems involving the allocation of limited resources.

2. What is the objective of linear programming?

The objective of linear programming is to find the values of decision variables that will minimize or maximize a given linear function, while satisfying all the constraints.

3. What is a global minimum in linear programming?

A global minimum in linear programming is the smallest possible value of the objective function that can be achieved by any feasible solution. It represents the optimal solution to the problem and is located at the lowest point on the objective function's graph.

4. How is linear programming used to solve real-world problems?

Linear programming is used to solve real-world problems by converting the problem into a mathematical model and then applying specific algorithms and techniques to find the optimal solution. It is commonly used in production planning, transportation and logistics, resource allocation, and financial planning, among others.

5. How do I solve a linear programming homework problem?

To solve a linear programming homework problem, you will need to first identify the objective function and all the constraints. Then, you can use graphical or algebraic methods to find the optimal solution. Alternatively, you can use software programs that are specifically designed to solve linear programming problems.

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