Re: Bug in NMaximize?

• To: mathgroup at smc.vnet.net
• Subject: [mg43506] Re: [mg43468] Bug in NMaximize?
• From: Michael Schreiber <michaelschreiber at mac.com>
• Date: Thu, 18 Sep 2003 05:39:54 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On Wednesday, Sep 17, 2003, at 14:00 Europe/Vienna, Guillermo Sanchez
wrote:

> Using:
>
> NMaximize[{x^2 + y^2, x^2/9 + y^2/4 <= 1}, {x, y}]
>
> Mathematica 5 gives as solution:
>
> {9., {x -> -3., y -> 3.242576952529308*^-19}}.
>
> Becouse it is a simetric problem (x^2 and y^2 >= 0) the true solution
> should be: x -> -3 and x -> +3.
>
> What is wrong?

x^2/9+y^2/4<1/.{x\[Rule]-3.`,y\[Rule]3.242576952529308`*^-19}
False

This is acceptable because the example used numerical approximation
with default options (lookup NMinimize for a discussion of options and
their consequences including ways to find multiple optima and many
examples).

x^2/9+y^2/4/.{x\[Rule]-3.`,y\[Rule]3.242576952529308`*^-19}
1.

Maximize should be used because it can solve this problem exactly; but
even if the same minimum is achieved at several points, only one is
returned:

Maximize[{x^2+y^2,x^2/9+y^2/4<=1},{x,y}]
{9,{x\[Rule]-3,y\[Rule]0}}

An extra condition produces the second maximum:

Maximize[{x^2+y^2,x^2/9+y^2/4<=1&&x>0},{x,y}]
{9,{y\[Rule]0,x\[Rule]3}}

>
> Guillermo Sanchez
>
>
M F Schreiber
Heimscholleg 26 Wien, A1130 Austria Europe
Michael at Schreiber.at

```

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