[Coin-discuss] problem of solving a model with SOS2 in CBC

[Hongxia Zhao]

Hello,

I am trying to solve the following simple problem with SOS2 constraint
using CBC,

------------------------------
min -10x1 + 5x2 -10x3

s.t. x1 + x2 + x3  = 2

     x1           <= 1

               x3 <= 1

     x1, x2, x3   >= 0

     { x1, x2, x3 } is SOS2
---------------------------------

I don't want to use binary variables to model the problem. So the MPS file
(sos.mps) of this problem is

*=============================================================
NAME           
ROWS
 N  obj     
 E  c1      
 L  c2      
 L  c3      
COLUMNS
    x1        obj                -10   c1                   1
    x1        c2                   1   
    x2        obj                  5   c1                   1 
    x3        obj                -10   c1                   1
    x3        c3                   1
RHS
    rhs       c1                   2   c2                   1 
    rhs       c3                   1  
SOS
 S2
    x1
    x2 
    x3  
ENDATA
*============================================================

I tried to solve this problem on windows by using CbcExamplesSample2.exe 

> CbcExamplesSample2.exe sos.mps

The solution I got has objective value -20 which is not correct. If the
SOS2 constraint was considered correctly, the solution should be 

x1 = x2 = 1, obj = -5.

My question is:

Can Cbc solve this kind of problem with SOS2 constraint and without using
binary variable correctly? If so, how?

Thanks,
Christy