maximizing multiple quadratic functions

I have multiple quadratic functions that I need to maximize subject to linear constraints. How can I do that in matlab. The problem is like this: Maximize: x1^2 + x2^2+...+xn^2

y1^2+y2^2+...+yn^2

z1^2+z2^2+...+zn^2 ............... subject to: F(x1,x2,...,y1,y2,..., z1,z2,...)<=1

G(x1,x2,...,y1,y2,...,z1,z2,....)=0

Where F and G are linear functions.

Answer 1

[Matt J]

Just call quadprog() multiple times.

[Maher]

I think quadprog() for convex functions and the functions here are nonconvex,but I can call fmincon. However how to call it multiple times? I write a loop, the variables are intermixing in the constraints function. Many thanks!

[Matt J]

You only have 3 objective functions. Just call it manually 3 times. No need for a loop.

Intermixing? They intermix in the objective function as well. Just assign zero coefficients to variables that don't participate in the objective function, e.g.,

 objective = x1^2+x2^2 +0*y1^2 +0*y2^2

[Maher]

Thank you!I'll do that and update you!

[Matt J]

You're welcome. If it solve the problem, though, please Accept-click the answer.

[Maher]

unfortunately it didn't work.

[Torsten]

Details ?

[Maher]

I didn't get a vector that attains a maximum value

[Torsten]

More details ? Code, e.g. ?