# Computational complexity for more general problems

When I read computational complexity I encounter problems like 3-SAT, set cover, knapsack. In the first two variables are discrete. In knapsack the weights and values are integer and all three problems have a combinatorial structure, what I mean is selecting a finite number from a finite set.

How about problems in continuous domains like finding the minimum or maximum of a function in real numbers? Or solving a differential equation to find a function? Can we prove that these problems too are hard or easy in a computational complexity sense?

Finally how do I know, by looking at a problem, if asking "is the problem NP-hard?" is a valid question?

• This related question may interest you.
– Raphael
Oct 1, 2014 at 20:19
• Sure, for example finding maximum likelihood estimate for a Gaussian mixture is NP-Hard. Oct 1, 2014 at 21:23
• Thanks, I believe in your example there is a combinatorial structure such as minimize distance between set of points.
– seek
Oct 2, 2014 at 2:35