Decision Optimization

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  • 1.  Cplex Error 5002, but problem should be solvable

    Posted Wed January 13, 2021 11:46 AM
    Hi, I have run into an issue with a QCQP where CPLEX gives "CPLEX Error 5002: objective is not convex.". However, the matrices in the problem are PSD, and any of the following modifications will result in CPLEX solving the problem without throwing an error:

    • Reformulating the problem along of vein of replacing (a+b)^2 in the objective with c^2, and adding an "c = a + b" constraint
    • Scaling every term in the objective down by a factor of 0.1
    • Scaling every term in the objective up by a factor of 10

    I am running with default CPLEX Interactive Optimizer settings, and am curious if anyone could provide some insight into this behavior.  I've boiled the problem into a small example, and have attached the original, reformulated, scaled-up, and scaled-down versions of the problem. Thanks!




    example_scaled_down.lp   403 B 1 version
    example_error.lp   408 B 1 version
    example_reformulated.lp   440 B 1 version
    example_scaled_up.lp   417 B 1 version

  • 2.  RE: Cplex Error 5002, but problem should be solvable

    IBM Champion
    Posted Wed January 13, 2021 06:26 PM
    I suspect you are dealing with rounding error issues. In your example, the Q matrix in the objective has two positive eigenvalues and one eigenvalue that equals zero ... give or take. Thanks to rounding error, CPLEX may be seeing a negative eigenvalue sufficiently different from zero to make the matrix look non-PSD. The various transformations you did would all change the eigenvalues, and apparently both scaling up and scaling down results in a third eigenvalue sufficiently close to zero to get by. So in the rounding error lottery, you were unlucky in one case and lucky in the others.

    Paul Rubin
    Professor Emeritus
    Michigan State University

  • 3.  RE: Cplex Error 5002, but problem should be solvable

    Posted Thu January 14, 2021 12:48 PM
    Thanks for your thoughts and insights Paul! Sounds very plausible to me.

    Michael Han