Thursday, October 11, 2012

GAMS/Gurobi QCP problems

Some quadratically constrained problems give incorrect results with GAMS/Gurobi:

variables z,x,y;
positive variables
e1.. z =g= x*x+y;
e2.. x+y =g= 1;

model m /all/
solve m minimizing z using qcp;

The reported solution:

**** OBJECTIVE VALUE                0.8750

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR z              -INF      0.812     +INF  3.834E-12
---- VAR x               .        0.250     +INF  3.945E-11
---- VAR y               .        0.750     +INF  1.186E-13

is not correct. Somehow Gurobi receives a different problem with an extra term in the objective:

  z + [ 2 x ^ 2 ] / 2
Subject To
e2: x + y >= 1
e1: z - y + [ - x ^ 2 ] >= 0
z free

At this moment I don't have a workaround for this. No doubt this will be fixed quickly and a GAMS update will be released. Keep an eye on for this.

Note: the LP file was generated by using an option file with writeprob xxx.lp. The documentation for this option in is somewhat terse. The type of file being written is determined by the extension. An lp file has a .lp extension, and similarly an mps file can be generated by using a file name of the form xxx.mps.

PS. the correct solution would be:

**** OBJECTIVE VALUE                0.7500

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR z              -INF      0.750     +INF       .
---- VAR x               .        0.500     +INF       .
---- VAR y               .        0.500     +INF       EPS

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