Given an NLO reduce it to unconstrained optimization problem

[ver_mathstats]

Homework Statement

We are required to reduce an unconstrained optimization problem. Problem is written below.

Relevant Equations

reduce to an unconstrained optimization problem

We are given the problem min x₃-x_4² such that (1): x₁² + x₃ = 2 and (2): (x₂-x₄)(x₂+x₄)=1.

What I did was solve for x₃ in (1) and then solve for x₄ in (2). I substituted those equations into min x₃-x_4² and I obtain the solution: 2-x₁²-x₂²+1, would this be the correct approach to this problem?

Thank you!

 

[Office_Shredder]

You wrote $x_{4^2}$ in a couple of places, is that supposed to be $x_4^2$?
I think you solved the problem just fine, but I would note literally solving for. $x_4$ requires writing down a $\pm$ which you have to carefully observe goes away when you square it, whereas solving for $x_4^2$ and substituting that does not.

Are you supposed to solve this? It's kind of weird, I think maybe they wanted you to maximize the function?

 

[ver_mathstats]

You wrote $x_{4^2}$ in a couple of places, is that supposed to be $x_4^2$?
I think you solved the problem just fine, but I would note literally solving for. $x_4$ requires writing down a $\pm$ which you have to carefully observe goes away when you square it, whereas solving for $x_4^2$ and substituting that does not.

Are you supposed to solve this? It's kind of weird, I think maybe they wanted you to maximize the function?

Yes I meant it to be the second one my apologies. No no, I just needed to reduce it and was making sure I was on the right track, we do not have to maximize it, the next part is to do DFP on the problem.

 

[Mark44]

@ver_mathstats, please don't write acronyms without explaining what they mean. For example, I guess that NLO stands for nonlinear optimization, but I have no idea what DFP stands for.

 

[ver_mathstats]

@ver_mathstats, please don't write acronyms without explaining what they mean. For example, I guess that NLO stands for nonlinear optimization, but I have no idea what DFP stands for.

Sorry I'm just so used to that, it's the David Fletcher Powell method.

 

[Mark44]

Sorry I'm just so used to that, it's the David Fletcher Powell method.

I'd be surprised if anyone at this site has heard of this guy, let alone would know what DFP stands for.