Implement the function `find_minimum(numbers)` that takes a list of integers `numbers` and returns the smallest value in the list. The list will contain at least one integer. You may not use the built-in `min()` function — implement the logic yourself using a loop and comparisons. The order of the list should not matter.
Constraints
The input list will contain at least one integer. The integers can be negative, zero, or positive. The function should run in O(n) time and O(1) extra space.