Imagine we have a square matrix with float values with $x$ rows and $x$ columns. We are to choose $x$ cells, such that the sum of the cells is as small as possible, but with the constraint that we can choose only one cell from each row, and only one cell from each column. How would one solve this?
It seems to me to be a discrete optimization problem, but while I am averse in continuous optimization I know basically nothing about discrete optimization. But I am not sure whether this can be solved differently than with discrete optimization.