We　focus　on　solving　the　clustered　Lasso　problem,　which　is　a　least　squares　problem　with　the　\ell1-type　penalties　imposed　on　both　the　coefficients　and　their　pairwise　differences　to　learn　the　group　structure　of　the　regression　parameters.　Here　we　first　reformulate　the　clustered　Lasso　regularizer　as　a　weighted　ordered-Lasso　regularizer,　which　is　essential　in　reducing　the　computational　cost　from　O(n2)　to　O(nlog(n)).　We　then　propose　an　inexact　semismooth　Newton　augmented　Lagrangian　(Ssnal)　algorithm　to　solve　the　clustered　Lasso　problem　or　its　dual　via　this　equivalent　formulation,　depending　on　whether　the　sample　size　is　larger　than　the　dimension　of　the　features.　An　essential　component　of　the　Ssnal　algorithm　is　the　computation　of　the　generalized　Jacobian　of　the　proximal　mapping　of　the　clustered　Lasso　regularizer.　Based　on　the　new　formulation,　we　derive　an　efficient　procedure　for　its　computation.　Comprehensive　results　on　the　global　convergence　and　local　linear　convergence　of　the　Ssnal　algorithm　are　established.　For　the　purpose　of　exposition　and　comparison,　we　also　summarize/design　several　first-order　methods　that　can　be　used　to　solve　the　problem　under　consideration,　but　with　the　key　improvement　from　the　new　formulation　of　the　clustered　Lasso　regularizer.　As　a　demonstration　of　the　applicability　of　our　algorithms,　numerical　experiments　on　the　clustered　Lasso　problem　are　performed.　The　experiments　show　that　the　Ssnal　algorithm　substantially　outperforms　the　best　alternative　algorithm　for　the　clustered　Lasso　problem.　©　2019　Society　for　Industrial　and　Applied　Mathematics