[cpgxiii]

Convex optimization can be a really amazing tool. We use optimization extensively, both on actually convex problems, and on non-convex-but-practically-solvable problems in robotics.

The math surrounding optimization is great; however, the reality of optimization tools is still very poor. A competitive optimizer is a massive project, and outside of a number of mostly limited/specialized solvers, the effective tools are all proprietary and very expensive (e.g. SNOPT, Gurobi, Mosek, CPLEX, etc). How solveable and stable your problems can be depends on these tools, and effective problem formulation (e.g. what and how many constraints you use, how you compute gradients) is essentially a black art learned through hard experience.

There's a great example of the complexity difference between optimization and other tools in the world of motion planning for robots: we expect that any semi-competent undergrad can implement search- and sampling-based planners (e.g. A* or RRT), implementing a good optimizer for trajectory optimization is a multi-million dollar project.

The world of optimization desperately needs a MuJoCo-DeepMind moment, where a large interested company buys one of the major commercial optimization providers and makes their tools free and open source. This would really be transformative to the field.