For many machine learning problems you can find an equivalent problem which is convex. This seems to be the method of choice for dealing with things like Suppor

For many machine learning problems you can find an equivalent problem which is convex. This seems to be the method of choice for dealing with things like Support Vector Machines. Many academics seem to dislike neural networks because of how easy it is to get stuck in local minima and how hard it is to say anything useful about the result. This won't happen with techniques based on convex optimization. Outside of machine learning solving a convex relaxation of a discrete optimization problem and then trying to round the result is one of the standard techniques in optimization. This is used all over the place, from straightforward linear relaxations for ILPs through the semidefinite relaxations of problems such as max cut. You start with an intractable problem, embed it into a tractable problem and use the result to gain information about the solutions to your original problem.