Choosing　optimal　hyper　parameters　for　Support　Vector　Machines(SVMs)　is　quite　difficult　but　extremely　essential　in　SVM　design.　This　is　usually　done　by　minimizing　estimates　of　generalization　error　such　as　the　k-fold　cross-validation　error　or　the　upper　bound　of　leave-one-out(LOO)　error.　However,　most　of　the　approaches　concentrate　on　the　dual　optimization　problem　of　SVM　In　this　paper,　we　would　like　to　consider　the　task　of　tuning　hyper　parameters　in　the　primal.　We　derive　a　smooth　validation　function　from　the　k-fold　cross-validation,　then　tune　hyperparameters　by　minimizing　the　smooth　validation　function　using　Quasi-Newton　optimization　technique.　Experimental　results　not　only　show　that　our　approach　is　much　faster　and　provides　more　precise　results　than　grid　search　method,　but　also　demonstrate　that　tuning　hyper　parameters　in　the　primal　would　be　more　efficient　than　in　the　dual　due　to　advantages　provided　by　the　primal.　©2010　IEEE.