Convex optimization

The class of problems of finding the best answer that have no false answers to get stuck on, so the true best can always be reached quickly.

When searching for the best answer that satisfies some conditions, a method can in general get caught at an answer that is only the best in its neighbourhood. If the problem is shaped like a bowl with a single bottom, a convex problem, then going downhill always arrives at the true bottom. An upper limit on the computing time can also be worked out in advance.

Calculating a trajectory to bring a rocket down under thrust onto a chosen spot is not convex as it stands. In 2007 Behçet Açıkmeşe and Scott Ploen showed that it can be rewritten in convex form without changing the answer^[1]. Because it can then be solved quickly and reliably, a computer on board can solve it over and over during the descent. The research was done for landing on Mars and was later used to land reusable rockets.