Originally posted by: sarahD

Hi!
I use the matlab interfaces (toolbox and API) for mixed integer quadratically constrained problems in CPLEX 12.2. I am not sure how to add quadratic constraints, if there is more than one.

1) For the Toolbox: How can I specify more than one matrix Q for cplexmiqcp.m ?
2) For API: How do I generate a higher dimensional struct array of the type cplex.Model.qc which I can then access using cplex.Model.qc(i)?

The examples given in the documentation unfortunately cover only single quadratic constraints!

Thanks a lot for your help!

Sarah
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: John Cui

Could you please refer to below thread:
http://www.ibm.com/developerworks/forums/thread.jspa?threadID=357875&tstart=0

John Cui
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: John Cui

For Cplex class, you can do like:

cplex=Cplex();
cplex.addCols([1 2 3]', [], [0 0 0]', [40 inf inf]');
cplex.addRows(-inf, [-1  1 1], 20);
cplex.addRows(-inf, [ 1 -3 1], 30);
cplex.addQCs([0 0 0]', [1 0 0;0 1 0;0 0 1], 'L', 1.0);
cplex.addQCs([0 0 0]', [1 0 0;0 1 0;0 0 1], 'L', 1.0,{'myqc2'});
cplex.addQCs([0 0 0]', [1 0 0;0 1 0;0 0 1], 'L', 1.0);
cplex.solve();

John Cui
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: John Cui

or

cplex.addQCs(
                 [0 0 0;1 0 0;0 1 0]',
                 {[1 0 0;0 1 0;0 0 1]
                  [1 0 0;0 1 0;0 0 1]
                  [1 0 0;0 1 0;0 0 1]},
                 'LLG',
                 [1.0 2.0 3.0],
                 {'qc1' 'qc2' 'qc3'});

John Cui
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: sarahD

Hi again,

First, thanks a lot, it works fine with addQCs for standard quadratic constraints. !

But I have another question:
As stated in the documentation, the solver detects socp constraints when given by quadratic constraints with matrices like
-1 0 0
0 1 0
0 0 1
although these matrices are nor positive semidefinite.
For my examples, this works just under certain circumstences, hence for a single socp constraint, and only in case that the first variable belongs to this socp constraint.

So, I works for one quadratic (socp) constraint with
l=0, r=0, Q=

-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

But not if I add a second matrix, eg:
l2=0, r2=0,
Q2 = 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

Or it also does not work for one constraint like
l=0, r=0, Q=

0 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

For the last two cases cplex states:
'CPLEX Error 5002: Q in 'q2' is not positive semi-definite.'

Can you help me? Is there a way to add several socp constraints?

Thanks a lot!!!
Best, Sarah
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: John Cui

What I just tried:

cplex=Cplex();
cplex.addCols([1 2 3]', [], [0 0 0]', [40 inf inf]');
cplex.addRows(-inf, [-1  1 1], 20);
cplex.addRows(-inf, [ 1 -3 1], 30);
cplex.addQCs([0 0 0]', [1 0 0;0 1 0;0 0 1], 'L', 1.0);
cplex.addQCs([0 0 0]', [0 0 0;0 -1 0;0 0 1], 'L', 0.0,{'myqc2'});
cplex.addQCs([0 0 0]', [-1 0 0;0 0 0;0 0 1], 'L', 0.0,{'myqc3'});
cplex.writeModel('qc.lp')
cplex.solve();

which works fine and export below lp file:

\Problem name: CPLEX
 
Minimize
 obj: x1 + 2 x2 + 3 x3
Subject To
 c1: - x1 + x2 + x3 <= 20
 c2: x1 - 3 x2 + x3 <= 30
 qc1:   [ x1 ^2 + x2 ^2 + x3 ^2 ] <= 1
 myqc2: [ - x2 ^2 + x3 ^2 ] <= 0
 myqc3: [ - x1 ^2 + x3 ^2 ] <= 0
Bounds
 0 <= x1 <= 40
End

You got the non-psd error, because your constraints are not PSD.

John Cui
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: sarahD

Hi!

Investigating the printed LP- model showed that the bounds got lost on the way in my program...
The quadratic constraint with Q=(-1000
0100
0010
0001)
is of course only an SOCP- constraints, if the first variable (with coefficient '-1') is nonnegative ;-)

Awesome, thanks again!

Best, Sarah
#CPLEXOptimizers
#DecisionOptimization