Alternating　direction　method　(ADM)　has　been　well　studied　in　the　context　of　linearly　constrained　convex　programming　problems.　Recently,　because　of　its　significant　efficiency　and　easy　implementation　in　novel　applications,　ADM　is　extended　to　the　case　where　the　number　of　separable　parts　is　a　finite　number.　The　algorithmic　framework　of　the　extended　method　consists　of　two　phases.　At　each　iteration,　it　first　produces　a　trial　point　by　using　the　usual　alternating　direction　scheme,　and　then　the　next　iterate　is　updated　by　using　a　distance-descent　direction　offered　by　the　trial　point.　The　generated　sequence　approaches　the　solution　set　monotonically　in　the　Fejér　sense,　and　the　method　is　called　alternating　direction-based　contraction　(ADBC)　method.　In　this　paper,　in　order　to　simplify　the　subproblems　in　the　first　phase,　we　add　a　proximal　term　to　the　objective　function　of　the　minimization　subproblems.　The　resulted　algorithm　is　called　proximal　alternating　direction-based　contraction　(PADBC)　methods.　In　addition,　we　present　different　linearized　versions　of　the　PADBC　methods　which　substantially　broaden　the　applicable　scope　of　the　ADBC　method.　All　the　presented　algorithms　are　guided　by　a　general　framework　of　the　contraction　methods　for　monotone　variational　inequalities,　and　thus,　the　convergence　follows　directly.　©　2010　Higher　Education　Press　and　Springer-Verlag　Berlin　Heidelberg.