Announcement from NA-Digest Volume 09 : Issue 38, 09-21-09:

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From: Bernard Beauzamy <bernard.beauzamy@scmsa.com> <br>
Date: Tue, 15 Sep 2009 10:34:58 -0400 <br>
Subject: Prize offered by SCM for efficient integration <br>

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The document "Robust Mathematical Methods for Extremely Rare Events"
<a href="http://www.scmsa.com/BB_rare_events_2009_08.pdf" >
http://www.scmsa.com/BB_rare_events_2009_08.pdf </a>
dated August 2009, by Bernard Beauzamy, uses the computation of a multiple 
integral, over a complicated domain in a many-dimensional space, in order to
estimate a probability. This approach is inherent to the method itself.

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However, the computation of the integral is done in a way which might not be
the best : the function to integrate is a polynomial in one variable (with 
degree >100 in our case), with rational coefficients (all coefficients are 
of the form m/n, where m and n are very large integers). In the paper, all 
coefficients are computed exactly, using the symbolic capabilities of Maple.

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Therefore, the integration is slow and requires considerable memory in the 
computer. Typically, at this point, our method requires 30 multiple 
integrations, each of which takes around 20 minutes on an ordinary computer.

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We would be interested to know if other numerical approaches are possible in
order to compute such multiple integrals, with sufficient accuracy. 

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We offer a prize of Euros 1,000 to the best solution : solution that can 
handle the requirements of speed, accuracy, and adaptability (not just our 
example, but any such example). Solutions may be provided by individuals or 
by teams.

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The solutions should be sent by email to scm.sa@orange.fr 
no later than March 31st, 2010.

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The best solution, besides the prize, will be posted on the "Robust 
Mathematical Modeling" web site and will be communicated to all participants
to the RMM program, worldwide (see 
<a href="http://www.scmsa.com/robust.htm">
href="http://www.scmsa.com/robust.htm</a>).