Some applications depend on approximately solving optimization problems that are hard even for small problems.
The poster child here is combinatorial optimization (more or less equivalently, np-complete problems), concrete examples are SMT solvers and their applications to software verification [1]. Non convex problems are sometimes similarly bad.
Non smooth and badly conditioned optimization problems scale much better with size, but getting high precision solutions is hard. These are important for simulations mentioned elsewhere, but not just for architecture and games, also for automating design, inspections etc [2].
Non smooth and badly conditioned optimization problems scale much better with size, but getting high precision solutions is hard. These are important for simulations mentioned elsewhere, but not just for architecture and games, also for automating design, inspections etc [2].
[1] https://ocamlpro.github.io/verification_for_dummies/
[2] https://www.youtube.com/watch?v=1ALvgx-smFI&t=14s