Optimization algorithms, which try to find the minimum values of mathematical functions, are everywhere in engineering. Among other things, they’re used to evaluate design tradeoffs, to assess control systems, and to find patterns in data.

One way to solve a difficult optimization problem is to first reduce it to a related but much simpler problem, then gradually add complexity back in, solving each new problem in turn and using its solution as a guide to solving the next one. This approach seems to work well in practice, but it’s never been characterized theoretically.

This month, at the International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Hossein Mobahi, a postdoc at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL), and John Fisher, a senior research scientist at CSAIL, describe a way to generate that sequence of simplified functions that guarantees the best approximation that the method can offer.

“There are some fundamental questions about this method that we answer for the first time,” Mobahi says. “For example, I told you that you start from a simple problem, but I didn’t tell you how you choose that simple problem. There are infinitely many functions you can start with. Which one is good? Even if I tell you what function to start with, there are infinitely many ways to transform that to your actual problem. And that transformation affects what you get at the end.” More here Analysis yields better optimization algorithms for engineering problems.