Prev: regression through a fixed point
Next: regression through a fixed point
From: Luis Felipe on 28 May 2010 17:04
Hi,

Have you ever seen this optimization problem ?
n
max prod (p_i)^a_i
i=1

n
subject to sum p_i = 1
i=1

where a_i is a positive constant for i=1,...,n

I would like to know if that optimization problem has any application
(or has been used to solve anything). Thank you for your comments.
From: us on 28 May 2010 17:08
Luis Felipe <luispipe16(a)gmail.com> wrote in message <8445cd34-c732-4010-aa1c-5a20d6b4b5cf(a)f14g2000vbn.googlegroups.com>...
> Hi,
>
> Have you ever seen this optimization problem ?
> n
> max prod (p_i)^a_i
> i=1
>
> n
> subject to sum p_i = 1
> i=1
>
> where a_i is a positive constant for i=1,...,n
>
> I would like to know if that optimization problem has any application
> (or has been used to solve anything). Thank you for your comments.

very nice, indeed... but: where's your problem with respect to CSSM (ML) (?)...

us
From: Walter Roberson on 28 May 2010 17:18
Luis Felipe wrote:

> Have you ever seen this optimization problem ?
> n
> max prod (p_i)^a_i
> i=1
>
> n
> subject to sum p_i = 1
> i=1
>
> where a_i is a positive constant for i=1,...,n

Your problem statement does not constrain p_i to be non-negative, leaving open
the possibility of using large negative and positive numbers.
From: Bruno Luong on 28 May 2010 17:21
Luis Felipe <luispipe16(a)gmail.com> wrote in message <8445cd34-c732-4010-aa1c-5a20d6b4b5cf(a)f14g2000vbn.googlegroups.com>...
> Hi,
>
> Have you ever seen this optimization problem ?
> n
> max prod (p_i)^a_i
> i=1
>
> n
> subject to sum p_i = 1
> i=1
>
> where a_i is a positive constant for i=1,...,n
>
> I would like to know if that optimization problem has any application
> (or has been used to solve anything). Thank you for your comments.

Not sure, but this is trivial to solve

Maximizing prod(p.*a) is equivalent to maximizing f(p) := sum(a*log(p))

The gradient of f is a./p.

The KTT condition tells us that

a./p = lambda*(1,1, ..).

Because sum(p) = 1, thus p = a/sum(a). We are done.

Bruno
From: us on 28 May 2010 17:22
Walter Roberson <roberson(a)hushmail.com> wrote in message <htpc0k$9o1$1(a)canopus.cc.umanitoba.ca>...
> Luis Felipe wrote:
>
> > Have you ever seen this optimization problem ?
> > n
> > max prod (p_i)^a_i
> > i=1
> >
> > n
> > subject to sum p_i = 1
> > i=1
> >
> > where a_i is a positive constant for i=1,...,n
>
> Your problem statement does not constrain p_i to be non-negative, leaving open
> the possibility of using large negative and positive numbers.

again,
very nice, indeed... but: where's your problem with respect to CSSM (ML) (?)...

us
 |  Next  |  Last
Pages: 1 2 3
Prev: regression through a fixed point
Next: regression through a fixed point