Learning about convex optimisation

The more I’m learning about optimisation problems, the more I am rediscovering my love for “ah ha” moments in mathematics. Like anyone from my generation, when I need to learn about a new topic I turn to YouTube. Fortunately for me, 3Blue1Brown, and his amazing Manim code, have significantly lowered the barrier to creating beautiful mathematical explainers.

I can now see how the simplex algorithm works in this video

or be guided through a clear narrative to motivate interior point methods here

Explainers such as these are intensely satisfying because the authors allow me to discover the concepts for myself. I don’t need to be force fed mathematical notation before we get to some grand reveal. In this case, I can appreciate how we have transformed a hard problem (the primal) into an easier one (the dual) which we can tackle with trusty solvers like Newton’s method.

Armed with this knowledge, I feel less intimated when I hear about Lagrange multipliers in other sources. I know, at a high level, we are just creating an equivalent problem that is easier to solve.

Shameless plug, but I have also used Manim to create a short video about my PhD. I entered it to a competition with a 3-minute limit, so it’s much faster paced than the videos above…