Summary: We present ALMA (Algorithm for Lagrange Multipliers Approximation), an iterative method for selecting tuning parameters in generalized LASSO problems for MRI reconstruction, which is a special case of l 1 -regularized least-square problem. Standardized approaches are often manual or heuristic; ALMA addresses this by approximating adaptatively Lagrange multipliers during reconstruction. On simulated MRI data, ALMA achieved mSSIM ≥ 0.99 and pSNR ≥ 40 dB, showing robust and near-optimal performance. Purpose: To introduce ALMA, a method for adaptatively computing tuning parameters in generalized LASSO problems during MRI reconstruction. Methods: We simulated MRI data using the Shepp-Logan phantom, testing ALMA across 450 reconstructions with varying undersampling (10–20%) and noise levels (3–7%). Image quality was assessed using mSSIM, pSNR, and CJV. Results: ALMA achieved average mSSIM of 0 .9951±0 .0041, pSNR of 42 .24±3 .42 dB, and CJV of 0 .0367±0 .0125, converging in about 7 .2±3 iterations. Conclusion: ALMA offers a reliable, automated alternative to manual tuning, producing high-quality reconstructions and showing promise for in vivo MRI applications.