I'm having trouble remembering the name of an algorithm I now am trying to reproduce.

The basics of the problem are as such:

- Given a finite set of a known length
- Look at the first item in the set.
- Choose whether to accept that value, or look at the next one
- Optimize for the best result, never being able to revisit prior values

So for instance, given a set of numbers [8,23,5,192,3,56,9,11,34,85,23,50,31,5], you are only able to "see" the first element in the list (8). It then needs to decide if that number is sufficient (let's assume we're optimizing for the max value) or if it should continue the search. If it accepts the value, the algorithm is finished, if it continues, it looks at 23, and makes the same assessment. This continues until a value is accepted or the list is complete, with the goal to have the algorithm score higher than random sampling.

Does anyone have the name for this problem, or better yet a wikipedia page for an algorithm to solve this problem?

Thanks in advance,

Motoma