Tuesday, 14:15 - 14:40 h, Room: H 2053


Arnold Neumaier
Projective methods for constraint satisfaction and global optimization

Coauthors: Ferenc Domes, Mihaly Markot, Hermann Schichl


Many constraint satisfaction problems and global optimization problems
contain some unbounded variables. Their solution by branch and bound
methods poses special challenges as the search region is infinitely
extended. Most branch and bound solvers add artificial bounds to make
the problem bounded, or require the user to add these. However, if
these bounds are too small, they may exclude a solution, while when
they are too large, the search in the resulting huge but bounded region
may be very inefficient. Moreover, global solvers that provide a
rigorous guarantee cannot accept such artificial bounds.
We present methods based on compactification and projective geometry
to cope with the unboundedness in a rigorous manner. Two different
versions of the basic idea, namely (i) projective constraint
propagation and (ii) projective transformation of the variables,
are implemented in the rigorous global solvers COCONUT and GloptLab.
Numerical tests demonstrate the capability of the new technique,
combined with standard pruning methods, to rigorously solve unbounded
global problems.


Talk 3 of the invited session Tue.2.H 2053
"Rigorous global optimization" [...]
Cluster 9
"Global optimization" [...]


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