My objective function is \left\| x \right\|^3 + f(y), where x=[x_1; x_2], f(y) is a convex function.

I know \left\| x \right\|^3 is convex, but how can I write \left\| x \right\|^3 in CVX ?

`square_pos(norm(x))`

I didnâ€™t get your point. As I know, square_pos(norm(x)) expresses \|x\|^2, however, my objective function is \|x\|^3.

Sorry, I misread the function.

You will benefit from reading http://cvxr.com/cvx/doc/funcref.html#new-functions .

help pow_pos

pow_pos Power of positive part.

pow_pos(X,P) = POS(X).^P = MAX(X,0).^P.

Both P and X must be real, and P must be greater than or equal to 1.`Disciplined convex programming information: pow_pos(X,P) is convex and nondecreasing in X; so when used in CVX expressions, X must be convex. P must be constant, real, and greater than or equal to 1.`

Thank you, this function works!