Optimization algorithms seek to find the minimum values of mathematical functions in engineering. It's how engineers evaluate design trade-offs, assess control systems and how people find patterns in data.
One practical 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.
If only someone could find a way to characterize optimization theoretically. You know, optimize it.