R help - Sep 2009 - Linear objective function with Quadratic constraints

I am new to R and I want to solve this following problem using R.

My Objective function is a linear function with Quadratic constraints.I want
to know how to solve this problem and which package will be helpful for me
for solving such type of problems.Moreover my one constraint is linear and
equality constraints and another quadratic constraint is inequality
constraint.
How to solve this problem ?
Plz help Me

Min z = 5 *x1 + 9*x2 + 7.15*x3 + 3.5 *x4
subject to following constraints.
x1 + x2 + x3 + x4 = 9
x1 + x4 <=6.55
x3(x3 - 3.6) >= 0 

 

 

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vikrant S wrote:
> 
> I am new to R and I want to solve this following problem using R.
> 
> My Objective function is a linear function with Quadratic constraints. I
> want to know how to solve this problem and which package will be helpful
> for me for solving such type of problems. Moreover my one constraint is
> linear and equality constraints and another quadratic constraint is
> inequality constraint.
> How to solve this problem ?
> Plz help Me
> 
> Min z = 5 *x1 + 9*x2 + 7.15*x3 + 3.5 *x4
> subject to following constraints.
> x1 + x2 + x3 + x4 = 9
> x1 + x4 <=6.55
> x3(x3 - 3.6) >= 0
> 
Your example is still not precise enough to force you away from linear
programming.

You have to assume lower bounds for the x_i, otherwise their is no minimum.

Say, x_i >= 0, then the quadratic constraint reduces to x3 >= 3.6 and you
are back to applying the simplex algorithm (e.g., the one in lpSolve). 
If your lower bound for x4 is a4 < 0, then solve two linear programs, one
for x4 >= 3.6 and one for a4 <= x4 <= 0.

You can even compute it manually by eliminating  x4 = 9 - x1 - x2 - x3.

--Hans Werner

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