I am having the following problem which I would like to solve using only excel functions without resorting to programming in vba or macros or manual commands.

I have a list of numbers in an array and I am looking for the minimal number in that array that satisfies some conditions, the conditions are such that they might exclude some cells in the array.
The ideal solution would have been a command like MINIF(range,condition) but such a function does not exist for MIN (it exists for counting COUNTIF)

How do I achieve the same result using other EXCEL functions?

Keep in mind that the array length and the conditions change dynamically during the run.