Huge 3D Minimum-distance controlled
perturbation intances
Instances contributed by Jordi Castro, obtained with the 3D tables generator.
They are convex separable quadratic problems. They are provided in extended
MPS format for quadratic problems. Section QUADOBJ/QSECTION/QUADS used
for quadratic terms. Choose the right keyword according to your solver
(i.e., the above are for Cplex-BPMPD/MOSEK/LoQo). The NL file generated by AMPL
is also provided. The difference in objective function between the NL and MPS
format is due to the constant coefficient in the quadratic function. Add
coefficient f0 (see below) to the solution with MPS
format for the true objective function.
10M variables and 210K
constraints instance. AMPL NL file is here . In a Sun Fire X2200
server
with AMD Opteron at 3.0 GHZ, and 32 GB of RAM, CPLEX11 required 28733 seconds
and 15GB RAM. The specialized interior-point code of, for instance, [ Castro07,
Castro03,Castro00]
only needed about 60 seconds and 1.2 GB RAM.
The optimal objective provided by CPLEX11 is
-2.6732194575e+12. The optimal objective provided by the specialized
interior-point method is -2673219457594.02. The constant of the
quadratic function is f0= 2673236903049.0.
An explanation of the good
behaviour of this approach in this kind of problems may be found in:
"J. Castro, J. Cuesta,
Quadratic regularizations in an interior-point method for primal
block-angular problems,
Mathematical Programming, 130 (2011) 415-445.
Previously appeared as
Research Report DR 2008/07,
Dept. of Statistics and Operations Research,
Universitat Politècnica de Catalunya, 2008.
"