Convex Least Squares Programming (CLSP) is a two-step estimator for solving underdetermined, ill-posed, or structurally constrained least-squares problems. It combines pseudoinverse-based estimation with convex-programming correction methods inspired by Lasso, Ridge, and Elastic Net to ensure numerical stability, constraint enforcement, and interpretability. The package also provides numerical stability analysis and CLSP-specific diagnostics, including partial R^2, normalized RMSE (NRMSE), Monte Carlo t-tests for mean NRMSE, and condition-number-based confidence bands.