Originally posted by: SystemAdmin

[sgdesmet said:]

I have a problem where the objective function looks like:

min(a*x_1 + b*x_2 + c*x_3 + d*x_1*x_2 + e*x_1*x_3)

x_i is a continuous variable in the range [0,1] Depending on the problem itself, the number of x_i may vary. Terms like x_i^2 wil never appear, and not necessarly every  x_i*x_j  combination will appear. The degree is always 2.

Since this quadratic problem is not solvable by cplex, is there a way to transform this function or approximate it to make it solvable?

Many Thanks.
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Originally posted by: SystemAdmin

[meson said:]

Hello,

Have you considered using an iterative approach by holding some of the x_i's constant? For example, you could change your objective to:

min(a*x_1 + b*x_2 + c*x_3 + d*x_1'*x_2 + e*x_1'*x_3)

where x_1' is x_1 from the previous iteration. There would be no guarantee of optimality though, and it is possible that it might not converge.

Hope it helps.

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Originally posted by: SystemAdmin

[sgdesmet said:]

I really need the optimal solution for my problem, and I think that using an iterative approach would produce a result which diverges to much from the optimal one. So I'm afraid I can't use such an approach.
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#MathematicalProgramming-General

Originally posted by: SystemAdmin

[prubin said:]

If your objective function is not convex, I'm not sure how you will find a probable global optimum, regardless of what software you pick.
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