I am minimising a diagonal quadratic matrix using CPLEX. All off diagonal elements are zero.
It has 500 variables and 20 linear constraints plus each variable is constrained to be within 0 and 1
All of the elements on the diagonal are greater than zero.
CPLEX complains that it is either not-optimal or unbounded depending on the values of the matrix.
I cannot see how this problem can be unbounded as it is a minimsation of a convex function. For some values CPLEX says that the solution is not optimal.
I have posted the lp file if that helps at ... http://speedy.sh/Ug76K/quadratic-fail.lp
Here is the CPLEX log
Tried aggregator 1 time.
QP Presolve eliminated 15 rows and 0 columns.
Reduced QP has 5 rows, 500 columns, and 1000 nonzeros.
Reduced QP objective Q matrix has 500 nonzeros.
Presolve time = 0.00 sec. (0.29 ticks)
Parallel mode: using up to 8 threads for barrier.
Number of nonzeros in lower triangle of A*A' = 10
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.00 sec. (0.00 ticks)
Summary statistics for Cholesky factor:
Threads = 8
Rows in Factor = 5
Integer space required = 5
Total non-zeros in factor = 15
Total FP ops to factor = 55
Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf
0 2.7831848e+014 -2.7831848e+014 6.65e+001 9.07e+002 5.57e+014
1 1.8149043e+012 -1.8149043e+012 5.37e+000 7.32e+001 4.49e+013
2 1.5035906e+012 -1.5035906e+012 4.89e+000 6.67e+001 4.09e+013
3 1.1322578e+012 -1.1322578e+012 4.24e+000 5.79e+001 3.55e+013
4 7.9610680e+011 -7.9610680e+011 3.56e+000 4.85e+001 2.98e+013
5 5.5016492e+011 -5.5016491e+011 2.96e+000 4.03e+001 2.47e+013
Barrier time = 0.00 sec. (0.96 ticks)
Total time on 8 threads = 0.00 sec. (0.96 ticks)
Status = 2
ERROR STATUS IS unbounded
Can anyone reproduce my problem using CPLEX ?
UPDATE: I have forced CPLEX to use the PRIMAL algorithm rather than the default. The optimiser now runs but I get a lot of "Markovitz threshold set to X.XX" style warnings.