The　generalized　convex　nearly　isotonic　regression　problem　addresses　a　least　squares　regression　model　that　incorporates　both　sparsity　and　monotonicity　constraints　on　the　regression　coefficients.　In　this　paper,　we　introduce　an　efficient　semismooth　Newton-based　augmented　Lagrangian　(Ssnal)　algorithm　to　solve　this　problem.　We　demonstrate　that,　under　reasonable　assumptions,　the　Ssnal　algorithm　achieves　global　convergence　and　exhibits　a　linear　convergence　rate.　Computationally,　we　derive　the　generalized　Jacobian　matrix　associated　with　the　proximal　mapping　of　the　generalized　convex　nearly　isotonic　regression　regularizer　and　leverage　the　second-order　sparsity　when　applying　the　semismooth　Newton　method　to　the　subproblems　in　the　Ssnal　algorithm.　Numerical　experiments　conducted　on　both　synthetic　and　real　datasets　clearly　demonstrate　that　our　algorithm　significantly　outperforms　first-order　methods　in　terms　of　efficiency　and　robustness.　©　2025　by　the　authors.