Utility theory and portfolio optimization: utility of what exactly?
In mean-variance optimisation I have typically seen the below quadratic utility function where $[]$ is the expected return (or mean return) of a possible portfolio, $\sigma^{2}$ is the return variance of that portfolio and $A$ is a parameter that the determines the sensitivity to variance.

$$=[]−\frac{1}{2}A\sigma^{2}$$

As an aside, maximising % return, also maximises $ return, log return and total wealth. They might not be equivalent when optimising for mean and variance though.