Nonlinear problem

Hi,

I am trying to minimize a function like f(x)=H1x+H2x^2+H3x^3

Can we really do it using cvx toolbox, ifnot can you suggest any best available tools for the problem.

If H1, H2, H3 are all input data (i.e., numbers) >= 0 (H1 need not be >= 0), you should be able to enter f(x) “as is” into CVX. Have you read the CVX Users’ Guide?

The H1,H2,H3 are the matrices made from the input data.

When writing higher powers of X, like X^2 etc I am getting disciplined program issue.

I was assuming that everything was scalars.

The first thing you need to do is to define s SCALAR objective function. That scalar function needs to be convex. If it is convex, it might be possible to use CVX, but not necessarily so.

If you have a scalar objective function, but it is not convex, you can consider using YALMIP. Until you have a scalar objective function, you are not ready to perform optimization.

Thank you, as mentioned X is a vector and H is a matrix.

If X is a vector, what is X^2 or X^3?

As I wrote above, the first thing you need to do is to define s SCALAR objective function.