Re: Constrained Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg57675] Re: Constrained Optimization
• From: dh <dh at metrohm.ch>
• Date: Fri, 3 Jun 2005 05:35:04 -0400 (EDT)
• References: <d7mj30\$bqm\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Caspar,
see below.
sincerely, Daniel

Caspar von Seckendorff wrote:
> Hi,
>
> I'd like to do constrained optimization with Mathematica 5.1 on a
> function that is defined piecewise. Unfortunately Maximize[] does not
> work  as I expected. A short & simple example to illustrate:
>
> f[x_,y_]:= (x-x^2) y
> Maximize[{f[x, y], 1/5 <= x <= 2/5, y > 0}, x]
Maximize is a numerical functions. Therefore, f[,] needs numeric input.
However, y is so far a puer symbol and has no numerical value. If I
understand your problem correctly, y is assumed to be a constant. But in
this case the maximum value depends on the unspecified y.
Mathematica gives you a correct error message.
>
> As a result I get:
> "The objective function (x-x^2) y contains a nonconstant expression y
> independent of variables {x}."
>
> Obviously for this Maximization, knowing that y > 0 I can do the
> following to get the desired value for x:
>
> Maximize[{x-x^2, 1/5 <= x <= 2/5}, x]
> Out[]= {6/25, {x -> 2/5}}
>
> Is there a way to achieve this without manual intervention? The reason
> is, that the functions I want to Maximize are defined Piecewise with
> several constraints...
>
> Thanks,
>
> -Caspar
>

```

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