Suppose that we have a function $L$ which is related to $\lambda$ and $\eta$ as follows:
$$L = \lambda + \rho(\eta - \bar{\eta})$$
where $\rho$ and $\bar\eta$ are constants.
It is said that the values of $\rho$ greater than zero implies convexity of $L$ with respect to eta. What does that mean exactly? I couldn't find a reasonable definition in the literature.