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We are formulating a QP optimization problem in Pyomo + Mosek (commercial).

Unexpectedly, mosek complains the quadratic coefficient is not PSD.

Error: rescode.err_obj_q_not_psd(1295): The quadratic coefficient matrix in the objective is not positive semidefinite as expected for a minimization problem.

Minimal reproducible example:

import pyomo.kernel as pmo
import numpy as np; np.random.seed(1)

n = 5
Q1 = np.random.randn(n, n)
Q1 = Q1.T @ Q1            # theoretically always PSD
m = 5
A1 = np.random.randn(m, n)
b1 = np.random.randn(m)

problem = pmo.block()

problem.x = pmo.variable_list()
for i in range(n):
    problem.x.append(pmo.variable())

problem.OBJ = pmo.objective(expr = problem.x @ Q1 @ problem.x, sense = pmo.minimize)

problem.cons = pmo.constraint_list()
tmp_lhs = A1 @ problem.x
for i in range(len(b1)):
    problem.cons.append(pmo.constraint(expr= tmp_lhs[i] <= b1[i]))

opt = pmo.SolverFactory("mosek")
opt.solve(problem)

Reasons we think Q1 is PSD:

  • All its eigenvalues are positive
  • CPLEX (commercial) is able to solve it

Kindly help!

pqrz
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  • I ran this with pyomo 5.7.3 and instead got "mosek.Error: rescode.err_qobj_upper_triangle(1415): Only elements in the lower triangle of the quadratic term in the objective should be specified. ". So there is possibly something fishy going on in the pyomo interface to Mosek, and perhaps something else fishy in your version. We'll try to check. – Michal Adamaszek May 14 '21 at 12:50
  • Which pyomo version are you using? – Michal Adamaszek May 14 '21 at 12:52
  • I can reproduce this with the latest release of Pyomo (5.7.3). However, it seems to have been fixed on the main dev branch, so it should be available in the next release. Likely fixed by this commit: https://github.com/Pyomo/pyomo/commit/09627b20e1baa73e3969077f271fbdfdc304dbc8 – Gabe Hackebeil May 14 '21 at 13:49
  • We are using pyomo v5.7.0 – pqrz May 17 '21 at 03:14
  • Utkarsh's answer's resolves this. Thanks Michal and Gabe! – pqrz May 17 '21 at 03:14

1 Answers1

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I fixed this bug in a PR back in Feb 2021. However, it seems that the current release (v 5.7.3) does not have the fix yet. You can do two things (for both of these you would need to know where pyomo is installed, find that out using print(pyomo.__file__) in the python console):

  1. Clone the Pyomo github repository (master branch) and use that as your pyomo installation. Hint: you can install pyomo using pip, and then replace the pyomo installation (somewhere in env/lib/site-packages/pyomo) with a symbolic link the repo clone. #lifehack

  2. If you have Pyomo 5.7.3 , then you can make the fix yourself. If you go to file: python3.8/site-packages/pyomo/solvers/plugins/solvers/mosek_direct.py then you only need to change line number 253 from mosek_qexp = (qsubi, qsubj, qvals) to mosek_qexp = (qsubj, qsubi, qvals).

The second option should be quicker.

Sorry for the inconvenience. It is a bit confusing why the release does not have this fix yet, but I will raise this issue with the maintainers of the repo.

Utkarsh Detha
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