The PRIMPING routine -- Tiling through proximal alternating linearized minimization. .. We introduce PAL-Tiling, a general framework to compute tilings according to a cost measure based on a theoretically founded numerical optimization technique. Requiring that the cost measure has a smooth relaxed function, which combines the matrix factorization error with a regularizing function, PAL-Tiling minimizes the relaxed objective under convergence guarantees. To simulate the minimization subject to the constraint that the matrices are binary, we derive a closed form of the proximal mapping with respect to a function which penalizes non-binary values. A thresholding to binary values according to the actual cost measure enables an automatic determination of the factorization rank.