how to write a rounding constraint for optimization

Question

I have an optimization problem as follows:

minimize $\sum_i \sum_j x_i x_j S_{ij}$

subject to the constraints:

$\sum_i x_i = 1 $

and

$x_i$ are rounded in increments of 0.01.

question is if there is a way I can implement the rounding constraint while still being within a continuous framework(i.e. using a computation library which can perform the computation with continuous $x_i$).

Thanks in advance.