▁R . ▁T yr rell ▁Rock af ell ar ▁in ▁relation ▁to ▁Fen ch el ▁du ality , ▁particularly ▁in ▁relation ▁to ▁proxim al - point ▁methods , ▁More au – Y os ida ▁regular ization , ▁and ▁maximal ▁monot one ▁operators : ▁These ▁methods ▁were ▁used ▁in ▁struct ural ▁optimization . ▁ ▁The ▁method ▁was ▁also ▁studied ▁by ▁Dim it ri ▁Bert se k as , ▁not ably ▁in ▁his ▁ 1 9 8 2 ▁book , ▁together ▁with ▁extensions ▁involving ▁non quad r atic ▁regular ization ▁functions , ▁such ▁as ▁ent rop ic ▁regular ization , ▁which ▁gives ▁rise ▁to ▁the ▁" ex pon ential ▁method ▁of ▁multip liers ," ▁a ▁method ▁that ▁handles ▁inequality ▁constraints ▁with ▁a ▁twice ▁differenti able ▁augment ed ▁L agr ang ian ▁function . ▁ ▁Since ▁the ▁ 1 9 7 0 s , ▁sequ ential ▁quadratic ▁programming ▁( S Q P ) ▁and ▁interior ▁point ▁methods ▁( IP M ) ▁have ▁had ▁increasing ▁attention , ▁in ▁part ▁because ▁they ▁more ▁easily ▁use ▁sparse ▁matrix ▁sub rout ines ▁from ▁numerical ▁software ▁libraries , ▁and ▁in ▁part ▁because ▁IP M s ▁have ▁proven ▁complexity ▁results ▁via ▁the ▁theory ▁of ▁self - con cord ant ▁functions . ▁The ▁augment ed ▁L agr ang ian ▁method ▁was ▁re ju ven ated ▁by ▁the ▁optimization ▁systems ▁L ANCE L OT ▁and ▁A MP L , ▁which ▁allowed ▁sparse ▁matrix ▁techniques ▁to ▁be ▁used ▁on ▁seem ingly ▁dense ▁but ▁" partial ly ▁separ able " ▁problems . ▁The ▁method ▁is ▁still