I'm running CPLEX (version 125) on MATLAB using the CPLEX API. I am trying to solve a Constrained Quadratic Programming problem, and I'm running into a primal infeasibility. In particular,the MATLAB code for the problem is:
[ystar, Jstar, flag, output]= ...
cplexqp(H, f, F, phi, G, gamma, ymin, ymax);
which corresponds to the problem:
ystar = argmin_y y'*H*y + f'*y
subject to:
ymin <= y <= ymax
G * y = gamma
F * y <= phi
However, the solution ystar returned by cplexqcp is such that:
max(F*ystar-phi) = 5.1854e-05
I would like to decrease this infeasibility gap. I tried to change the primal feasibility bound, but it seems it doesn't have any effect:
ops=cplexoptimset('cplex');
ops.feasopt.tolerance=1e-7;
How can I configure the solver so as to level the infeasibility? The solver gives the following diagnostic messages:
Number of nonzeros in lower triangle of Q = 2622
Using Approximate Minimum Degree ordering
Summary statistics for factor of Q:
Rows in Factor = 4248
Integer space required = 4362
Total non-zeros in factor = 27048
Total FP ops to factor = 334848
Tried aggregator 1 time.
QP Presolve eliminated 1128 rows and 114 columns.
Aggregator did 80 substitutions.
Reduced QP has 7984 rows, 8302 columns, and 129418 nonzeros.
Reduced QP objective Q matrix has 4134 nonzeros.
Parallel mode: using up to 8 threads for barrier.
Number of nonzeros in lower triangle of A*A' = 433356
Using Approximate Minimum Degree ordering
Summary statistics for Cholesky factor:
Threads = 8
Rows in Factor = 7984
Integer space required = 32473
Total non-zeros in factor = 556316
Total FP ops to factor = 62101602
Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf
0 1.6154270e+04 -1.8807064e+06 1.92e+06 2.77e+05 5.03e+06
1 1.7649880e+06 -4.6190853e+06 5.23e+05 7.57e+04 1.37e+06
2 1.8883665e+06 -4.8518299e+06 1.30e+05 1.89e+04 3.42e+05
3 8.3385088e+05 -2.9607988e+06 2.05e+04 2.97e+03 5.39e+04
... (some lines are omitted for brevity)
31 9.9411620e+01 9.9411598e+01 1.10e-08 9.27e-10 4.32e-08
32 9.9411615e+01 9.9411611e+01 1.37e-08 1.47e-10 6.85e-09
33 9.9411614e+01 9.9411614e+01 2.19e-08 6.10e-12 2.51e-08
Barrier time = 1.91 sec. (361.06 ticks)
Total time on 8 threads = 1.91 sec. (361.06 ticks)
So it seems that the primal infeasibility of the solution is 2.19e-08; however, it seems that the solution is not that feasible.
Update: I normalised the equality and inequality constraints as follows:
F = F ./ kron( ones(1,size(F,2)), abs(phi) );
phi = sign(phi);
(Note: no element of phi is zero or near-zero. This way, all elements of phi become either 1 or -1.) and
for i=1:numel(gamma)
if (abs(gamma(i))>1e-4)
G(i,:) = G(i,:)/abs(gamma(i));
gamma(i) = sign(gamma(i));
end
end
The infeasibility I'm getting now is 5.577e-07 calculated as max(F*ystar-phi) (for the updated normalised matrices F and phi). Is CPLEX using an interior-point solver? If yes, there shouldn't be any infeasibility.
Update 2: I have uploaded the data for this problem and a test case HERE.
