I have constructed a function in Matlab that is convex and increasing (qualitatively similar to an exponential function but I am hoping to avoid the successive approximation requirement of exp). In my specification of the function I take a minimum of two convex functions which of course does not, in general, result in a convex function; however for the functions I am using, the result is convex. My function is

```
function y = cost( x )
y = min( inv_pos( -x ), max( square_pos( x + 3 )/4, 1 ) );
```

For those unfamiliar with CVX syntax, the function is min( 1/max(-x,0), max(max(x+3,0)^2/4, 1) ). CVX throws the error:

```
Disciplined convex programming error:
Cannot perform the operation min( {convex}, {convex} )
```

Is there any way to convince CVX that my function is indeed convex? Talking to it hasn’t been working.

Thanks