Re: Re: Constrained Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg57700] Re: [mg57686] Re: Constrained Optimization
• From: Andrzej Kozlowski <andrzej at akikoz.net>
• Date: Sun, 5 Jun 2005 04:17:43 -0400 (EDT)
• References: <d7mj30\$bqm\$1@smc.vnet.net> <d7pb7q\$t80\$1@smc.vnet.net> <200506040704.DAA11789@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 4 Jun 2005, at 16:04, Caspar von Seckendorff wrote:

> *This message was transferred with a trial version of CommuniGate
> (tm) Pro*
> Thanks to all for your replies,
>
> Your're right "y" was meant to be an unknown constant. As I understand
> it know, Maximize[] does some sort of numerical optimization. I
> thought
> it would be able to use some concave Programming logic (like
> Kuhn-Tucker) to solve this problem for me, returning a list of
> possible
> optima in symbolic form together with the neccessary constraints...
> But
> I admit that maybe this is to much to ask for ;-)
>
> Greetings,
>
> -Capar

Actually, it seems you are not asking for too much. Just that
Maximize is not the function to use.

This is how you do it:

f[x_, a_] := (x - x^2) a

Resolve[ForAll[z, 1/5 <= z <= 2/5, 1/5 <= x <= 2/5 &&
f[z, a] <= f[x, a]]]

(a < 0 && x == 1/5) || (a == 0 && 1/5 <= x <= 2/5) ||
(a > 0 && x == 2/5)

Is this what you had in mind?

Andrzej Kozlowski

Chiba, Japan

```

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