Gurobi “Objective Q not PSD ” for Convex quadratic problem #338
Description
I got this error when using Gurobi 9.0.1 in Julia 1.3.1: Gurobi.GurobiError(10020, "Objective Q not PSD (diagonal adjustment of 5.8e-01 would be required)")
However, I'm sure that my problem is convex, as you can see from the code below:
F=eigen(testM)
@show minimum(F.values)
which gives a positive minimum eigenvalue of my 50 by 50 matrix testM, minimum(F.values) = 0.01262644537861781.
Now the following code produces the "not PSD" error:
psdm = Model(solver=GurobiSolver(OutputFlag=0))
@variable(psdm, t[1:50] )
@objective(psdm, Min, dot(t,testM*t))
@constraint(psdm, dot(t,t) <= 1)
status = solve(psdm)
As you can see, the problem is a convex quadratic problem. Why is Gurobi saying it is not PSD?
Thank you!
The matrix testM is given below:
50×50 Array{Float64,2}:
2.59448e11 -8.8763e11 -5.8729e11 … 3.03758e11 -5.82268e11
-8.8763e11 3.03678e12 2.00926e12 -1.03922e12 1.99207e12
-5.8729e11 2.00926e12 1.3294e12 -6.87592e11 1.31803e12
-1.55914e12 5.33416e12 3.52929e12 -1.82542e12 3.4991e12
-6.05552e10 2.07173e11 1.37074e11 -7.08972e10 1.35901e11
-1.8582e12 6.35734e12 4.20627e12 … -2.17556e12 4.17029e12
2.74024e11 -9.37498e11 -6.20285e11 3.20823e11 -6.14981e11
5.94194e11 -2.03287e12 -1.34503e12 6.95675e11 -1.33353e12
-1.58152e12 5.41076e12 3.57997e12 -1.85163e12 3.54935e12
9.69765e10 -3.31779e11 -2.19518e11 1.13539e11 -2.1764e11
9.56474e10 -3.27232e11 -2.16509e11 … 1.11983e11 -2.14658e11
5.00434e11 -1.7121e12 -1.13279e12 5.85901e11 -1.1231e12
-1.57677e10 5.39448e10 3.5692e10 -1.84606e10 3.53867e10
⋮ ⋱
2.19594e12 -7.51281e12 -4.97077e12 2.57097e12 -4.92825e12
8.05208e11 -2.7548e12 -1.82268e12 9.42727e11 -1.8071e12
2.92622e12 -1.00113e13 -6.62384e12 … 3.42598e12 -6.56719e12
1.05624e12 -3.61362e12 -2.39091e12 1.23663e12 -2.37047e12
1.67725e12 -5.73824e12 -3.79664e12 1.9637e12 -3.76417e12
-7.68743e11 2.63004e12 1.74014e12 -9.00034e11 1.72526e12
8.41691e11 -2.87962e12 -1.90527e12 9.85441e11 -1.88897e12
-2.26199e12 7.73879e12 5.12028e12 … -2.64831e12 5.07649e12
-9.90114e11 3.38741e12 2.24124e12 -1.15921e12 2.22207e12
-6.62424e11 2.2663e12 1.49947e12 -7.75557e11 1.48665e12
3.03758e11 -1.03922e12 -6.87592e11 3.55636e11 -6.81711e11
-5.82268e11 1.99207e12 1.31803e12 -6.81711e11 1.30676e12
I also post this issue here: https://discourse.julialang.org/t/gurobi-objective-q-not-psd-for-convex-quadratic-problem/42689