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MathGroup Archive 1998

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Re: Re: Global max for a nonlinear function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15212] Re: [mg15125] Re: Global max for a nonlinear function
  • From: "Nicolas B.E. Sawyer" <nbes at eee.nott.ac.uk>
  • Date: Tue, 22 Dec 1998 04:01:42 -0500
  • Organization: University of Nottingham
  • References: <74o11e$49e@smc.vnet.net> <199812160811.DAA24442@smc.vnet.net.> <367AD056.E37FFDCB@suu.edu>
  • Sender: owner-wri-mathgroup at wolfram.com

I agree I should be using FindMinimum[] within my functions, but your
missing the main point.

Without using FindMinimum[] I can tell you that there are also maxima in
Sin[x] at 9Pi/2, 13Pi/2, 17Pi/2 ... nicely spaced at intervals of 2Pi.
However, where are ALL the maxima for Sin[x^2] between 0 and 2Pi?

findMaxima[Sin[x^2], {x, 0, 2 Pi}]

Out[40]=
{{1.25331, 1.}, {2.8025, 1.}, {3.75994, 1.}, {4.51889, 1.}, {5.16755,
1.}, {5.74341, 1.}, {6.26657, 1.}}

Suppose I throw in a Bessel function or two for good measure. What would
be your initial estimates then? How would you know whether you'd missed
a result here or there?

I'm manipulating experimental data and want to find the maxima and
minima, with their positions, in interpolations and equation fits to
results. I could do this by plotting my results and reading off the
points I'm interested in. My functions effectively automate this
process.

Finally, to Wolfram, it would be nice if FindMaximum[] existed. We
aren't expected to do Cos[x-Pi/2] to get Sin[x] so why do we have to do
FindMinimum[-f[x],...] and reverse the sign of the result to get a
maximum?

Des Penny wrote:
> 
> Hi Nicolas:
> The FindMinimum command already does what is needed, i.e. it can be used to
> find the max of a given function.  Thus, to find the max of Sin[x], just
> find the min of -Sin[x]:
> 
> In[1]:=
> FindMinimum[-Sin[x],{x,0}]
> Out[1]=
> {-1.,{x\[Rule]1.5708}}
> In[2]:=
> FindMinimum[-Sin[x],{x,3 Pi}]
> Out[2]=
> {-1.,{x\[Rule]7.85398}}
> 
> Cheers,
> 
> Des Penny
> Physical Science Dept
> Southern Utah University
> Cedar City, Utah 84720
> 
> Voice: (435) 586-7708
> FAX: (435) 865-8051
> Email: penny at suu.edu
> 
> Nicolas B.E. Sawyer wrote:
> 
> > mukul chawla wrote:
> > >
> > > I am trying to compute the global maxima for a nonlinear function
> > > subject to a set of constraints, is there a way to do that using
> > > mathematica ?? If so, how ??
> > >
> > > Thanks,
> > > Mukul
> >
> > I've written some code for finding the maxima and minima of a function
> > by looking for zeros in the first differential. It extracts candidate
> > points (using FullGraphics[]) from the data generated by Plot[] and
> > returns a list of the maxima or minima found within a plotted range
> >
> > e.g.
> >
> > findMaxima[Sin[x], {x, 0, 4 Pi}]
> >
> > gives
> >
> > Out[1]=
> > {{1.5708, 1.}, {7.85398, 1.}}
> >
> > I'd like to submit the code to MathSource but think it needs testing and
> > possibly tidying up first. I don't consider myself to be an expert in
> > Mathematica programming, so would like a hand with this. If you would
> > like to help, please get in touch.
> >
> > --
> > Nicolas B.E. Sawyer
> >
> > Department of Electrical and Electronic Engineering, University of
> > Nottingham,
> > University Park,
> > Nottingham,
> > NG7 2RD.
> >
> > Tel: +44 115 9515151 ext 12028
> > Fax: +44 115 9515616
> >
> > E-mail: nbes at eee.nottingham.ac.uk

-- 
Nicolas B.E. Sawyer


Department of Electrical and Electronic Engineering, University of
Nottingham,
University Park,
Nottingham,
NG7 2RD.

Tel: +44 115 9515151 ext 12028
Fax: +44 115 9515616

E-mail: nbes at eee.nottingham.ac.uk


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