In　this　work,　we　develop　a　simple　yet　practical　algorithm　for　solving　nonlinear　optimization　problems　by　finding　a　root　of　a　real　function　f　¢(x)　with　a　good　local　convergence.　The　algorithm　can　be　easily　implemented　in　software　packages　for　achieving　desired　convergence　orders.　For　the　general　n　-point　formula,the　order　of　convergence　rate　of　the　presented　algorithm　is　n　t,　the　unique　positive　root　of　the　equation　xn-xn-1--x-1=0　©　(2013)　Trans　Tech　Publications,　Switzerland.