Re: Plot vs NMaximize
- To: mathgroup at smc.vnet.net
- Subject: [mg94317] Re: Plot vs NMaximize
- From: Nikolaus Rath <Nikolaus at rath.org>
- Date: Wed, 10 Dec 2008 04:47:54 -0500 (EST)
- References: <ghlmm5$ko7$1@smc.vnet.net>
Bill Rowe <readnews at sbcglobal.net> writes:
> On 12/8/08 at 6:22 AM, Nikolaus at rath.org (Nikolaus Rath) wrote:
>
>>It seems to me that it is significantly faster *and* more accurate
>>to determine global maxima by plotting the function and looking for
>>the positions on the plot than to use NMaximize: in all the cases
>>that I've encountered recently, NMaximize got stuck in local extrema
>>(which was very easy to see when looking at the plot).
>
>>I know that global optimization is a very difficult problem, but I
>>do not understand why Plot[] does not suffer from the same problem.
>>If Plot[] is able to generate a plot where I can see the position of
>>the global maximum in a second, why does NMaximize need several
>>seconds to get stuck in some local maxima? Shouldn't it be able to
>>make use of the same algorithms that Plot[] uses?
>
> In short, no. The algorithms in Plot say nothing whatever about
> either maxima or minima. All the plot algorithm does is sample
> your function and display points at each sampled position
> connecting them with lines. In absolutely no case, does this say
> anything about a maximum or minimum. It is only your
> interpretation of the resulting graphic that assigns
> maximum/minimum to the plot. The points you see as
> maximum/minimum are in no way different from any other plotted
> point from the perspective of the algorithms used in Plot.
>
> An effective way to use NMaximize, is to first Plot the function
> and use that plot to specify the search range to be used with
> NMaximize (at least for the 1-D problem).
I fully agree. But my question is: why doesn't NMaximize do this
automatically? It seems like a very sensible thing to do.
Best,
-Nikolaus
--
=C2=BBIt is not worth an intelligent man's time to be in the majority.
By definition, there are already enough people to do that.=C2=AB
-J.H. Hardy
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