I am trying to minimize numerically (over the reals) a polynomial S
with rational coefficients.
The function sage.numerical.optimize.minimize() returns without
returning a value.
Here's the relevant fragment of Sage code (executed using the menu
item 'evaluate all')
===== BEGIN CODE FRAGMENT =====================================
N
44
# RQ = PolynomialRing(QQ, N, 'x', sparse=True); # this was executed
earlier
S in RQ
True
print 'S is a polynomial over Q in', len(S.variables()), 'variables';
print 'S is a quartic polynomial';
print 'S contains', len(S.coefficients()), 'terms';
S is a polynomial over Q in 44 variables
S is a quartic polynomial
S contains 55188 terms
S_exp =SR(S);
init_values = [0] * len(S_exp.variables());
soln=sage.numerical.optimize.minimize(S_exp,init_values);
soln
Traceback (click to the left of this block for traceback)
...
NameError: name 'soln' is not defined
===== END OF CODE FRAGMENT =====================================
This does not happen for a smaller problem:
S is a polynomial over Q in 40 variables
S is a quartic polynomial
S contains 34766 terms
i.e., minimize() does successfully return a value.
I'm running Sage Version 4.4.4 under OS X 10.6.4 on a macbookpro with
4GB RAM, acquired in the form
sage-4.4.4-OSX-64bit-10.6-i386-Darwin.dmg
I would attach the worksheet itself to this posting, if I saw a way to
do so.
Any help would be much appreciated. Also any pointers towards a more
efficient method to minimize such polynomials. I'm just starting to
learn Sage and Python. At the moment, the bottlenecks appear to be
the conversion to a symbolic expression, 'S_exp =SR(S); ' and the
execution of minimize(). The polynomial algebra used to construct S
executes relatively quickly. The number of variables is of the form
N=4mn where m and n are positive integers. I'd like to take N slightly
larger, though I don't expect that my computing resources will allow
taking N much larger, even if I use a more efficient method to
minimize S.
thanks,
Daniel Friedan
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