[R] Quadratic Constraints

[vikrant S]

HI All,
I am unable to solve a optimization Problem Please Help Me out of this to
solve. The Optimization problem is as follows :- 
My objective function is linear and one of the constraint is quadratic. 

Min z = 5 * X1 + 9* X2  + 7.15 *X3 + 2 * X4
subject to
 X1 + X2 + X3 +X4  = 9
 X1  + X4 < = 6.55
 X3(X3 - 3.5) >=0
 X1,X2,X3,X4 >=0
 Now the problem is how to solve this kind of problem. Which package should
be used to handle such problems. Please explain with an example. 
Another problem is that I have to cases to  be solve in this problem.
case 1:-) If X3 = 0
case 2 :-) If X3 > 0 then X3 > 3.6
I want to handle both this case in one problem so the quadratic constraints
is written
The thing is that I want to evaluate my objective function for both cases
and which ever is optimum that solution i need,
Here I don't want to use the If Else condition and repeat the program. IS
there any other better way in which i could solve this problem?
If not please try to provide me the solution for my original problem having
a quadratic constraint.
-- 
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