Originally posted by: SystemAdmin

I'm a beginer and I'm using cplex solving the problem below:
P=500-∑q*q+5
This is a cost function, the problem I need to solve is:
Maximize P.
How to solve this problem? This function is not linear, can cplex solve this problem? Is that mean I need to solve it with piecewise linear and quadratic method?

Many Thanks,
Alex
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Originally posted by: SystemAdmin

First of all, you can of course discard the constant terms from your objective function and solve "max -sum(q_i^2)". Btw: do you really mean "500" and "5", or is one of them missing a linear "q" term?

The objective function is convex. Thus, you can solve the problem with CPLEX. You do not need piecewise linear functions, you can directly include the quadratic objective function. On the other hand, if it is okay to model the objective function as a piecewise linear function (with only a small number of pieces), and you have integer variables in your model anyway, then you may get better performance with the piecewise linear approach since then this is a MIP rather than a MIQP.
Tobias
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Originally posted by: SystemAdmin

Thanks, Tobias. But I think I gave a incorrect question before, the result is to find the area under the p curve rather than computing p given q.

For computing the area under the p curve, is that mean I need to break up the quadratic function into a piecewise linear which can give me a new quadratic function. Is there any examples can explain this problem clearly?
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Originally posted by: SystemAdmin

So you would like to maximize the integral of some (parametric?) function such that the parameters satisfy certain constraints?

I guess you should first try to formulate the task in a mathematically precise way. Maybe, you can just write down the integral as a closed formula.
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