It is a rather theoretical question to better understand some definitions.
Can descision variables in descrete optimization problems be only integers? If I have a set of real numbers which are not only natural numbers is it a continious optimization problem?
An example of a problem:
If there is a set of variables:
| animal | value |
|---|---|
| frog | 0.54 |
| cat | -9.12 |
| duck | 0.001 |
| dog | 4 |
| snake | -300.09 |
is that a continious or descrete problem?
From the Wiki definition: A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of values. For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. The reason is that any range of real numbers between a and b with a , b ∈ R ; a ≠ b is uncountable. A variable is a discrete variable if and only if there exists a one-to-one correspondence between this variable and N, the set of natural numbers.
Theoretically I could say that the example is a non-empty range of real numbers between -300.09 and 4 and see it is a continuous problem. From the Wikipedia definition I understand that descrete variables must belong to a set of natural numbers, so it is not my case. Or do I undestand it wrong?