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Puzzle with Maximize

• To: mathgroup at smc.vnet.net
• Subject: [mg74220] Puzzle with Maximize
• From: Holger Meinhardt <Holger.Meinhardt at wiwi.uni-karlsruhe.de>
• Date: Wed, 14 Mar 2007 03:59:27 -0500 (EST)

Hi,

I am in the process of tracking down a problem with the computing
time related to the command Maximize[] I encountered for long time
in my Mathematica Package TuGames.

http://library.wolfram.com/infocenter/MathSource/5709/

With Workbench I was now able to find
out what caused the huge difference in computation time I observed
between the old command ConstrainedMax[] and Maximize[], but due
to the information I got with Workbench, I could not locate the
source of the problem. I have enclosed the relevant piece of output
generated with Profile[]. My function needed, for instance on a Xeon
with 3.0 GHz Mathematica 5.2 under Linux, more than 15421.5 seconds
to complete correctly with Maximize[], whereas using the old command
ConstrainedMax[] the job was completed in 2.4 seconds. Any idea was 
going wrong according to the output generated by Profile[]?

   Calls  |        Time   |  Evaluation
--------------------------------------------------------------------------------------------------------------------------------
        1 |      15420.16 |  Which[callm === False, 
ConstrainedMax[objfunc, nb, var], True, Maximize[Prepend[nb, objfunc], 
var]]
        1 |      15420.16 |  Maximize[Prepend[nb, objfunc], var]
576914980 |        320.19 |  0
211701672 |        121.11 |  False
162049360 |         90.76 |  Null
62065676 |         35.60 |  True
59037977 |         33.44 |  1
34952094 |         19.36 |  2
32026952 |         17.95 |  3


Regards,
Holger Meinhardt