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From: Tolja on 9 May 2010 16:08
Hi,

I need to find the maximum of the following function:

f(w1, w2) = | h1*w1 + h2*w2 | + | h3*w1 + h4*w2 |

where h1,h2,h3,h4 are complex constants and w1,w2 are complex
variables.
The additional constraint is |w1|<=1 and |w2|<=1.
(|.| is the absolute value or modulus)

If this is too complicated to be solved I can change the constraint
into: |w1|=|w2|=1, i.e. only the phase of the complex variables can be
modified.

Thank you.
From: Hero on 10 May 2010 10:09
Tolja wrote:
> Hi,
>
> I need to find the maximum of the following function:
>
> f(w1, w2) = | h1*w1 + h2*w2 | + | h3*w1 + h4*w2 |
>
> where h1,h2,h3,h4 are complex constants and w1,w2 are complex
> variables.
> The additional constraint is |w1|<=1 and |w2|<=1.
> (|.| is the absolute value or modulus)
>
> If this is too complicated to be solved I can change the constraint
> into: |w1|=|w2|=1, i.e. only the phase of the complex variables can be
> modified.
>

This is equivalent to:
there are two length on the x-axis: h11 and h33
and there are two length h22 and h44 at an angle @ resp ß.
We look for one angle € applied as a rotation to @ as well as to ß,
so that | ( h11, 0 ) + (h22, @ + € ) | + | ( h33, 0 ) + ( h44, ß + € )
|
yields its maximum.

With friendly greetings
Hero
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