Re: Re: Problem with element and Maximize
- To: mathgroup at smc.vnet.net
- Subject: [mg82875] Re: [mg82846] Re: Problem with element and Maximize
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Fri, 2 Nov 2007 03:26:01 -0500 (EST)
- References: <4209462.1193744482571.JavaMail.root@m35> <fg9pgk$mtl$1@smc.vnet.net> <305444.1193931692764.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
What Maximize "tries for" depends on what methods are available, which in
turn depends on the type of coefficients used. Or rather... each method
does what it CAN do.
Bobby
On Thu, 01 Nov 2007 05:14:08 -0500, Uncle Paul <paul at desinc.com> wrote:
>> Don't round the real-valued solution; it won't always get you the best
>> integer solution.
>>
>> But this should work:
>>
>> data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}};
>> eq = Fit[data, {1, x, x^2, x^3}, x]
>> proxy = Rationalize[eq, 10^-15]
>> Maximize[{proxy, x \[Element] Integers, x <= 20}, x]
>> eq /. Last@%
>>
>> 1.96128*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3
>>
>> 1/509872338168900 + (10 x)/3 - (3 x^2)/10 + x^3/150
>>
>> {5567805932804389/509872338168900, {x -> 7}}
>>
>> 10.92
>>
>> Without the upper bound the function has no maximum and, with
>> approximate
>> coefficients, Maximize can't use efficient integer optimization methods.
>>
>
> I don't disagree this works. There are two issues with this, though.
>
> The unbounded answer of 5 indicates it is trying for local maxima,
> something I would expect.
>
> The second issue is I would expect one of three possibilities. If I
> ask a mathemetician, I would expect either a local maxima or
> +infinity. If I ask software, I would expect local maxima, +infinity
> or a complaint. An incorrect answer without complaint is confusing.
>
> Cool technique with Rationalize[] though. I'll have to remember that
> one.
>
> Paul
>
>
--
DrMajorBob at bigfoot.com