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Let's consider a problem where all edge costs are greater than zero, but not above some $\epsilon$: Image a problem where we have an infinite path where the first edge is cost $\frac{1}{2}$, the next is $\frac{1}{4}$, the following is $\frac{1}{8}$, and so on forever. Every edge is greater than zero, meeting the condition being proposed in the question. ...


1

No, they are prone to get stuck in local maxima, unless the whole search space is investigated. A simple algorithm will only ever move upwards; if you imagine you're in a mountain range, this will not get you very far, as you will need to go down before going up higher. You can see that going down a bit will have a net benefit, but the search algorithm will ...


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