Originally posted by: adai

I face a problem as nonconvex nonlinear programming problem.

the objective function and all the other constraints is linear except the following inequation:

-c~ij~ (x~i~-x~j~)^2^+-c~ij~a~i~a~j~(x~i~-x~j~)+c~ij~a~i~a~j~<=0, i,j=1,2,...M

can this nonconvex nonlinear problem be solved by CPLEX?
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Originally posted by: SystemAdmin

No, CPLEX cannot solve non-convex problems with the exception of the integrality condition.

But sometimes it is possible to model a non-convex MINLP as a MIP. For example, if all of your quadratic terms x*y contain at least one binary variable, say x, then you can model the term as

x = 0 -> q = 0 x = 1 -> q = y

and use q instead of x*y in your model. Note that the code above is using indicator constraints. CPLEX will automatically generate the corresponding big-M formulation, if it thinks that this is better. But of course you can model this with big-M yourself.
Tobias
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