A　class　of　non-smooth　convex　optimization　problems　which　arise　naturally　from　applications　in　sparse　group　Lasso,　have　attracted　significant　research　efforts　for　parameters　selection.　For　given　parameters　of　the　problem,　proximal　gradient　method　(PGM)　is　effective　to　solve　it　with　linear　convergence　rate　and　the　closed　form　solution　can　be　obtained　at　each　iteration.　However,　in　many　practical　applications,　the　selection　of　the　parameters　not　only　affects　the　quality　of　solution,　but　also　even　determines　whether　the　solution　is　right　or　not.　In　this　paper,　we　study　a　new　method　to　analyse　the　impact　of　the　parameters　on　PGM　algorithm　to　solve　the　non-smooth　convex　optimization　problem.　We　present　the　sensitivity　analysis　on　the　output　of　an　optimization　algorithm　over　parameter,　and　show　the　advantage　of　the　technique　using　automatic　differentiation.　Then,　we　propose　a　hybrid　algorithm　for　selecting　the　optimal　parameter　based　on　the　method　of　PGM.　The　numerical　results　show　that　the　proposed　method　is　effective　for　the　solving　of　sparse　signal　recovery　problem.