I feel software/CS people largely avoid (or don’t need) certain areas of math. To me, convex optimization is more the domain of engineering when there are cont

I feel software/CS people largely avoid (or don’t need) certain areas of math. 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.