Originally posted by: SystemAdmin
CPLEX handles only linear and convex quadratic objectives, so if your objective is quadratic (and convex for a minimization/concave for a maximization), you'll need to find a different software package.
If your objective is quadratic and meets the convexity condition, you could try a cutting plane approach. Create a variable z and maximize or minimize it, whichever is appropriate, subject to your constraints (which will initially not contain z). You'll need to bound z above (maximizing) or below (minimizing). As each "solution" is encountered, you'll need to generate not just the objective value but a supporting hyperplane of the objective function and add that as a constraint. That may require numerical differentiation on your part.
Back in the vacuum tube era, I seem to remember cutting plane methods having a reputation for slow convergence. My guess is that, even with a suitable quadratic objective, you might be better served by a nonlinear optimization program.
Paul
Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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