The objective function is surely convex as its second derivative is (6x*(2x^3 + 1))/(x^3 - 1)^3 which is positive if x>1. However, the cvx failed to optimize the problem. How can I deal with the function? A test code is shoed as follows
cvx_begin
variable x;
minimize inv_pos(x^3-1);
subject to
x>=1;
y<=10;
x+y<=3;
cvx_end

Thank you for replying. I’m sorry that my example may be not appropriate. What about this objective function? It is still convex. But cvx failed to solve it. How can I optimize it?
cvx_begin
variable x;
variable y;
minimize inv_pos(pow_p(x,3)-1)+inv_pos(pow_p(y,3)-1);
subject to
x>=1;
y>=1;
x+y<=3;
cvx_end
Here is the error message