i.

I just recently heard about PROC INTPOINT, the specialized new procedure

for linear programming that has been included in SAS/OR since release 8.1.

I only have a more or less nodding acquaintance with the details of

interior point methodology for linear programming, but I was told that PROC

INTPOINT was fast, and could handle larger, more complex LPs than PROC LP,

so I thought I'd check it out.

Here are logs from the same input matrix (in sparse format) to both procs.

For this problem, it took some tuning (e.g., in the numbers of iterations

and time allowed) to get both procedures to run to completion...

PROC INTPOINT output:

420 proc intpoint condata = SFD.SO04_S26_USE03_lpm_2s

421 conout = SFD.SO04_S26_USE03_lpm_2io_d

422 sparsedata

423 bytes = 100000000

424 maxiterb = 1999

425 rttol = 1E-12

426 maximize

427 ;

428 run ;

NOTE: Number of variables= 86372 .

NOTE: Number of <= constraints= 4 .

NOTE: Number of == constraints= 0 .

NOTE: Number of >= constraints= 21741 .

NOTE: Number of constraint coefficients= 259116 .

NOTE: 21745 columns, 0 rows and 21745 coefficients were added to the

problem to handle

unrestricted variables, variables that are split, and constraint

slack or surplus

variables.

NOTE: There are 172892 nonzero elements in A * A transpose.

NOTE: Of the 21745 rows and columns, 21733 are sparse.

NOTE: There are 173504 nonzero superdiagonal elements in the sparse rows of

the factored A * A

transpose. This includes fill-in.

NOTE: There are 466836 operations of the form u[i,j]=u[i,j]-u[q,j]*u[q,i]/u

[q,q] to factorize

the sparse rows of A * A transpose.

NOTE: The Primal-Dual Predictor-Corrector Interior Point algorithm

performed 1346 iterations.

NOTE: Objective= 885896.14315.

NOTE: The data set SFD.SO04_S26_USE03_LPM_2IO_D has 86372 observations and

6 variables.

NOTE: There were 453607 observations read from the data set

SFD.SO04_S26_USE03_LPM_2S.

NOTE: PROCEDURE INTPOINT used:

real time 15:00.58

cpu time 14:26.05

PROC LP output:

518 proc lp data = SFD.SO04_S26_USE03_lpm_2s

519 primalout = SFD.SO04_S26_USE03_lpm_2o_d

520 sparsedata

521 preprocess

522 MAXIT1=99999

523 MAXIT2=99999

524 epsilon = 1E-4

525 time = 4800

526 ;

527 * print best ; * evidently only for integer soln ;

528

529 run ;

NOTE: Preprocessing 1 ...

NOTE: 10 constraints eliminated.

NOTE: 86372 upper bounds decreased.

NOTE: Preprocessing 2 ...

NOTE: Preprocessing done.

NOTE: The data set SFD.SO04_S26_USE03_LPM_2O_D has 108119 observations and

10 variables.

NOTE: PROCEDURE LP used:

real time 50:36.25

cpu time 47:56.57

530

531 %put _ORLP_ = ;

_ORLP_ =

532 %put &_ORLP_. ;

STATUS=SUCCESSFUL PHASE=2 OBJECTIVE=577043483485.813 P_FEAS=YES D_FEAS=YES

PHASE1_ITER=22795

PHASE2_ITER=20209 PHASE3_ITER=0

533

534 quit / save ;

535

536 quit ;

PROC INTPOINT certainly did go faster, by a factor of three in this case,

but I know the data well enough to say that the result of PROC LP looks

correct, and the r

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