Dear Visitor,
In this directory you can find some problems which are difficult
to solve, at least with interior point methods. Basically, modelling
mistakes made these problems "crazy". But, these problems are excelent
examples to test numerical robustnes of a solver and observe numerically
bad behavior.
Here are short stories about these problems:
de063155
de063157
These problems comes from an early version of the water
management system Aquarius, developed at TU Delft. By building
the optimization problem, almost every modelling mistakes were
happen, for example wrong measurements which resulted in extreme
large and small coefficients. No tolerances were used by the
computation of the matrix values. Actually, I found that these
problems are unsolvable by most of the solvers.
A note: the large values in the RHS are not to be ignored, those
constaints are binding at the optimum !
de080285 Similar to the previous two problems. Very small values are
presented in the matrix, which "blow-up" the model if scaling
is applied. Additionally (which, I believe more strange for IPMs),
for some of the free variables a lower bound -10000.0 was introduced.
gen
gen1
gen2
gen4
These problems are approximations in L1 norm and come from
image reconstruction problems. Some of them were created by
using fixed point format, which resulted in different relative
accuracy in the coefficients (I believe, this is the source
of the extreme numerical instability). The problems are
additionally degenerate and it is very difficult to solve them
to 8-digit accuracy.
l30 Originally a convex optimization problem, but formulated as
LP. Many free variables, heavy fill-in.
iprob Created artifically. All variables are free. Very badly
conditioned. Optimal value (by exact aritmetic) has to be
2990.00
ADDITIONS ARE WELCOME !
Csaba Meszaros,
meszaros@sztaki.hu