Lagrange Multiplier for discrete variables

Question

I haven't formulated my problem formally yet. But, the goal is to minimize the squared error i.e. $ (L - \sum_{i=1}^{N}{w_{i}l_{i}})^2$ where $l_{i}$ are constants, $w_{i}$ are weights to be optimized. Weight can only take values in binary space i.e. 0/1. Is there any way to run the optimization on these kinds of problems? I understand that I can formulate the constraints in the form $w_{i}(w_{i}-1) = 0$. But, it leads to exponential number of solutions which are intractable when N is very large.