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. "