Originally posted by: Yassin_86

Dear,

However, I have a maximization model with a quadratic objective function, I get an error message of " Q in objective is not positive semi definite". The form I have used is like;

Regards,
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Originally posted by: SystemAdmin

As the message indicates, it looks like your model's Q matrix is not positive semi definite (the condition of xTQix ≥ 0 irrespective of the feasibility of x is not being satisfied). You will need to change this matrix appropriately to make it positive semi-definite.

Assuming that your model is a QP, if you are using CPLEX Optimization Studio 12.3, there is a new feature to help solve in-definite QPs which involves the setting of the IloCplex::SolutionTarget (CPX_PARAM_SOLUTIONTARGET) parameter. More about this feature can be found under the following doc link:

http://publib.boulder.ibm.com/infocenter/cosinfoc/v12r3/index.jsp?topic=%2Filog.odms.studio.help%2FContent%2FOptimization%2FDocumentation%2FOptimization_Studio%2F_pubskel%2Fps_COS_Eclipse7.html
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Originally posted by: EdKlotz

> Yassin_86 wrote:
> Dear,
>
> However, I have a maximization model with a quadratic objective function, I get an error message of " Q in objective is not positive semi definite". The form I have used is like;
>
> Regards,
CPLEX gives only a single error message when the Q matrix is indefinite. Since CPLEX internally solves minimization problems, the message is that Q is not positive semi definite,
rather than the negative semi definite concavity requirement for maximization problems.

In this case, the action you should take depends on your situation. If you truly want to solve a model with an indefinite Q matrix, follow Abhishek's instructions to take advantage of the indefinite Q matrix solver available starting with CPLEX 12.3. On the
other hand, if you believe your Q matrix should be positive or negative semi definite, then you need to determine why it is not. Some tools and techniques to help you do this appear on the IBM support site.
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