The Linear Programming via Regularized Least Squares (LPPinv) is a two-stage estimation method that reformulates linear programs as structured least-squares problems. Based on the Convex Least Squares Programming (CLSP) framework, LPPinv solves linear inequality, equality, and bound constraints by (1) constructing a canonical constraint system and computing a pseudoinverse projection, followed by (2) a convex-programming correction stage to refine the solution under additional regularization (e.g., Lasso, Ridge, or Elastic Net). LPPinv is intended for underdetermined and ill-posed linear problems, for which standard solvers fail.