(
optimization,
computer science:)
The replacement of
discrete constraints with
continuous ones in a problem (and solving that instead).
Integer constraint problems (optimising when one or more variables are constrained to be integers) are notoriously difficult: integer programming (which is linear programming with integer variables) is NP hard, whereas we know how to solve linear programming in polynomial time. So it can make sense simply to remove all integer constraints from variables, and seek an optimal solution with fractional values. Rounding appropriately, the result can be considered an approximation to the integer problem.