Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: An optimization problem
Replies: 19   Last Post: Sep 14, 2013 9:44 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Percival

Posts: 1,299
Registered: 10/25/10
Re: An optimization problem
Posted: Sep 8, 2013 9:01 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

quasi wrote:
> Peter Percival wrote:
>> quasi wrote:

>>>
>>> No, that's not automatic -- it requires proof.

>>
>> Indeed so. What I meant when I said it was clear is that the
>> proof is very simple and can be be done in ones head.
>>
>> For simplicity's sake let n = 2, x_1 = y and x_2 = z, then my
>> claim is that if
>>
>> (1 + y^2 + z^2)/(1 + y + z)
>>
>> has a minimum, then y = z there. Why is that clear? Because
>> if it weren't so then
>>
>> (1 + y^2 + z^2)/(1 + y + z) =/= (1 + z^2 + y^2)/(1 + z + y).

>
> No, your appeal to symmetry doesn't support your claim unless
> you know that there is a _unique_ point in R^2 for which the
> function achieves a minimum.


Silly me! What a foolish mistake to make.

> If all you know is that the function f is symmetric in the
> variables y and z and that f achieves a global minimum value
> somewhere in the domain, that's not enough to conclude that
> the global minimum value can be achieved at some point for
> which y = z.
>
> quasi
>



--
Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.