## LPnetlib/lp_stair

Netlib LP problem stair: minimize c'*x, where Ax=b, lo<=x<=hi
Name lp_stair LPnetlib 691 356 614 4,003 4,003 Linear Programming Problem No M. Saunders D. Gay
Structural Rank 356 true 1 1 0 0% 0% no no real
SVD Statistics
Matrix Norm 1.464861e+01
Minimum Singular Value 2.564993e-01
Condition Number 5.710977e+01
Rank 356
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download ```A Netlib LP problem, in lp/data. For more information send email to netlib@ornl.gov with the message: send index from lp send readme from lp/data send minos from lp/data ------------------------------------------------------------------------------ This LP problem is the source of four sparse matrices in the Harwell/Boeing sparse matrix collection: STR_0, STR_200, STR_400, and STR_600. Those four matrices are square, nonsingular basis matrices that occured during the solution of STAIR. ------------------------------------------------------------------------------ The following are relevant excerpts from lp/data/readme (by David M. Gay): The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude slack and surplus columns and the right-hand side vector, but include the cost row. We have omitted other free rows and all but the first right-hand side vector, as noted below. The byte count is for the MPS compressed file; it includes a newline character at the end of each line. These files start with a blank initial line intended to prevent mail programs from discarding any of the data. The BR column indicates whether a problem has bounds or ranges: B stands for "has bounds", R for "has ranges". The BOUND-TYPE TABLE below shows the bound types present in those problems that have bounds. The optimal value is from MINOS version 5.3 (of Sept. 1988) running on a VAX with default options. PROBLEM SUMMARY TABLE Name Rows Cols Nonzeros Bytes BR Optimal Value STAIR 357 467 3857 27405 B -2.5126695119E+02 BOUND-TYPE TABLE STAIR UP FX FR From Michael Saunders, Systems Optimization Laboratory at Stanford University. When included in Netlib: Explicit zeros omitted; cost coefficients negated. The following are relevant excerts from lp/data/minos (by Michael Saunders), regarding experience with MINOS 5.0 on the problems he provided: (unscaled) (scaled) File Name Rows Cols Elems Optimal Objective Itns Time Itns Time ---- -------- ---- ---- ----- ----------------- ---- ---- ---- ---- 11. STAIR 357 467 3867 2.5126695E+02 MAX 519 15.7 389 13.1 * Objective is the first row of type N. It is minimized except as shown. * Itns is the number of iterations required to solve the problem by the primal simplex method, as implemented in the Fortran code MINOS 5.0 (May 1985), using default values for all parameters. (The initial basis is triangular.) * Time is the processor time required on an IBM 3081K. The MINOS source code was compiled with the IBM Fortran 77 compiler VS FORTRAN, using the options NOSDUMP, NOSYM and OPT(3).```