Anecdotally it seems like most software engineers have heard of linear programming, but very few have heard of convex programming [1], and fewer still can apply it. The fixation on LPs is kind of odd ...
It is probably just a “git gud” situation. I even re-read Lars Blackmore’s “Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem” from time to time hoping that i find a way to apply a similar convexification idea to my problems. With all of that I’m not that surprised that convex optimisation is not more widely known.
To me, convex optimization is more the domain of engineering when there are continuous functions and/or stochastic processes involved.
Much of signal processing and digital communication systems are founded around convex optimization because it’s actually a sensible way to concretely answer “was this designed right?”.
One can use basic logic to prove a geometry proof, or the behavior of a distributed algorithm.
But if one wants to prove that a digital filter was designed properly for random/variable inputs, it leads to finding solutions of convex optimization problems (minimization of mean squared error or such).
Of course, whether the right problem is being solved is a different issue. MMSE is just mathematically extremely convenient but not necessarily the most meaningful characterization of behavior.