▁ ▁References ▁ ▁External ▁links ▁▁ <0x09> <0x09> ▁Category : National ▁Register ▁of ▁Historic ▁Places ▁in ▁Cache ▁County , ▁Ut ah ▁Category : V ict or ian ▁architecture ▁in ▁Ut ah ▁Category : Build ings ▁and ▁structures ▁completed ▁in ▁ 1 8 9 7 <0x0A> </s> ▁Aug ment ed ▁L agr ang ian ▁methods ▁are ▁a ▁certain ▁class ▁of ▁algorithms ▁for ▁solving ▁const rained ▁optimization ▁problems . ▁ ▁They ▁have ▁similar ities ▁to ▁penalty ▁methods ▁in ▁that ▁they ▁replace ▁a ▁const rained ▁optimization ▁problem ▁by ▁a ▁series ▁of ▁un const rained ▁problems ▁and ▁add ▁a ▁penalty ▁term ▁to ▁the ▁objective ; ▁the ▁difference ▁is ▁that ▁the ▁augment ed ▁L agr ang ian ▁method ▁adds ▁yet ▁another ▁term , ▁designed ▁to ▁m im ic ▁a ▁Lag range ▁multip lier . ▁ ▁The ▁augment ed ▁L agr ang ian ▁is ▁not ▁the ▁same ▁as ▁the ▁method ▁of ▁Lag range ▁multip liers . ▁ ▁View ed ▁differently , ▁the ▁un const rained ▁objective ▁is ▁the ▁L agr ang ian ▁of ▁the ▁const rained ▁problem , ▁with ▁an ▁additional ▁penalty ▁term ▁( the ▁augment ation ). ▁ ▁The ▁method ▁was ▁originally ▁known ▁as ▁the ▁method ▁of ▁multip liers , ▁and ▁was ▁studied ▁much ▁in ▁the ▁ 1 9 7 0 ▁and ▁ 1 9 8 0 s ▁as ▁a ▁good ▁alternative ▁to ▁penalty ▁methods . ▁It ▁was ▁first ▁discussed ▁by ▁Magn us ▁H est enes ▁in ▁ 1 9 6 9 ▁and ▁by ▁Pow ell ▁in ▁ 1 9 6 9 . ▁The ▁method ▁was ▁studied ▁by