[Fwd: Re: GLPK Dualprices]

[Andrew Makhorin]

-------- Forwarded Message --------
From: Andrew Makhorin <mao@gnu.org>
To: Harald Mumm <harald.mumm@hs-wismar.de>
Subject: Re: GLPK Dualprices
Date: Sun, 29 May 2022 19:36:20 +0300

> Hi Harald,
> 
> 
> On Sun, 2022-05-29 at 08:39 +0200, Harald Mumm wrote:
> > Hallo Andrew,
> > 
> > is it possible, that GLPK sometimes calculates wrong dual prices?
> > 
> > I send you an example  in the attachment,  where CPLEX calculates
> > 
> > other dual prices than GLPK.
> 
> Please note that LP may have multiple optimal solutions (in degenerate
> cases). This means that some constraint which happen to be active at
> one
> optimum point may be inactive at other optimum point.
> 
> I solved your LP with glpsol:
> 
> 
> GLPSOL--GLPK LP/MIP Solver 5.0
> Parameter(s) specified in the command line:
>  --lp masterg.lp
> Reading problem data from 'masterg.lp'...
> 46 rows, 17 columns, 62 non-zeros
> 77 lines were read
> GLPK Simplex Optimizer 5.0
> 46 rows, 17 columns, 62 non-zeros
> Preprocessing...
> ~     0: obj =   3.527760000e+03  infeas =  0.000e+00
> OPTIMAL SOLUTION FOUND BY LP PREPROCESSOR
> Time used:   0.0 secs
> Memory used: 0.0 Mb (45669 bytes)
> 
> 
> Since the optimal objective value is the same as for cplex, there is
> no
> error. You also may see this from KKT optimality conditions:
> 
> 
> Karush-Kuhn-Tucker optimality conditions:
> 
> KKT.PE: max.abs.err = 0.00e+00 on row 0
>         max.rel.err = 0.00e+00 on row 0
>         High quality
> 
> KKT.PB: max.abs.err = 0.00e+00 on row 0
>         max.rel.err = 0.00e+00 on row 0
>         High quality
> 
> KKT.DE: max.abs.err = 0.00e+00 on column 0
>         max.rel.err = 0.00e+00 on column 0
>         High quality
> 
> KKT.DB: max.abs.err = 0.00e+00 on row 0
>         max.rel.err = 0.00e+00 on row 0
>         High quality
> 
> 
> Best,
> 
> Andrew Makhorin
> 
> 
> > 
> > Sincerely yours
> > 
> > Harald, University of Applied Sciences, Wismar  Germany
> > 
> > 
> > PS CPLEX Dualprices:
> > 
> > Dual simplex - Optimal:  Objective =  3.5277600000e+03
> > Solution time =    0.02 sec.  Iterations = 0 (0)
> > Deterministic time = 0.02 ticks  (1.47 ticks/sec)
> > 
> > CPLEX> display solution dual *
> > Constraint Name             Dual Price
> > c1                          141.550000
> > c2                          330.530000
> > c3                          318.280000
> > c5                          201.940000
> > c7                          237.010000
> > c8                          283.710000
> > c9                          143.440000
> > c10                         221.820000
> > c11                         130.990000
> > c12                         210.350000
> > c13                         205.530000
> > c14                         175.150000
> > c15                         231.340000
> > c17                         155.250000
> > c21                         192.060000
> > c25                         204.170000
> > c41                         144.640000
> > All other dual prices matching '*' are 0.
> > 
> > PS GLPK Dualprices
> > 
> > c1 = 0.0
> > c2 = 0.0
> > c3 = 0.0
> > c4 = 0.0
> > c5 = 0.0
> > c6 = 0.0
> > c7 = 0.0
> > c8 = 0.0
> > c9 = 0.0
> > c10 = 0.0
> > c11 = 0.0
> > c12 = 0.0
> > c13 = 0.0
> > c14 = 0.0
> > c15 = 0.0
> > c16 = 0.0
> > c17 = 0.0
> > c18 = 0.0
> > c19 = 0.0
> > c20 = 0.0
> > c21 = 0.0
> > c22 = 0.0
> > c23 = 0.0
> > c24 = 0.0
> > c25 = 0.0
> > c26 = 0.0
> > c27 = 0.0
> > c28 = 0.0
> > c29 = 0.0
> > c30 = 0.0
> > c31 = 0.0
> > c32 = 0.0
> > c33 = 0.0
> > c34 = 0.0
> > c35 = 0.0
> > c36 = 0.0
> > c37 = 0.0
> > c38 = 0.0
> > c39 = 0.0
> > c40 = 0.0
> > c41 = 0.0
> > c42 = 0.0
> > c43 = 0.0
> > c44 = 0.0
> > c45 = 0.0
> > c46 = 330.53