Originally posted by: student2902

I create a model as follows:

Minimize
 obj: IloX2
Subject To
 IloC0: IloX0 + IloX1  = 5
 IloC1: IloX0 - IloX2 + IloX3 <= 0
 IloC0: - 2 IloX0 + [ IloX0 ^2 ] >= 0
 IloC1: - 2 IloX1 + [ IloX1 ^2 ] >= 0
Bounds
 0 <= IloX0 <= 5
 0 <= IloX1 <= 5
 0 <= IloX2 <= 100
 0 <= IloX3 <= 100
End

but the Solver return that there's no solution. I think the right solution is IloX2 = 0.
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Originally posted by: SystemAdmin

Please check the solver status and error codes. CPLEX doesn't prove that the model is infeasible. There is no solution, because CPLEX cannot solve the model. The two quadratic constraints are not positive semi-definite.

In your case, however, you can simplify the model. Because all variables are non-negative, the quadratic constraints -2x + x^2 >= 0 are equivalent to (x >= 2 or x = 0). So, instead of writing quadratic constraints you can specify IloX0 and IloX1 to be semi-continuous variables with domain 2,5. "Semi-continuous" means that the variable can either be 0 or inside the specified interval.
Tobias
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Originally posted by: student2902

Thank Tobias. I did it and CPLEX solve problem easily.
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