I work on convex optimization with Stephen Boyd's book.
As an example, support vector machines are mentioned as an application of separating hyperplanes theorem. I am wondering if there is any other application of convex optimization to artificial intelligence.
I am very unaware of AI methods, but as far as I know it involves minimizing functions. Does any of them involve minimizing a convex (or quasi-convex, log-convex) function?
Convex optimization is a very important area in Machine learning as convex functions have very nice properties (local minima is global minima). It is important to identify when a cost function is convex or not. If it isn't convex, we could probably convert it to a convex one.
A lot of engineering problems can be written as optimization problems and solved using convex optimization.
SVMs, Linear regression are use-case examples of convex optimization. Check the following for more info,