Computationally efficient tools for fitting generalized linear model with convex or non-convex penalty. Users can enjoy the superior statistical property of non-convex penalty such as SCAD and MCP which has significantly less estimation error and overfitting compared to convex penalty such as lasso and ridge. Computation is handled by multi-stage convex relaxation and the PathwIse CAlibrated Sparse Shooting algOrithm (PICASSO) which exploits warm start initialization, active set updating, and strong rule for coordinate preselection to boost computation, and attains a linear convergence to a unique sparse local optimum with optimal statistical properties. The computation is memory-optimized using the sparse matrix output.