Fortheimprovedtwo-sidedprojectedquasi-Newtonalgorithms,whichwerepresentedinPartI,weproveinthispaperthattheyarelocallyone-steportwo-stepsuperlinearlyconvergent.Numericaltestsarereportedthereafter.ResultsbysolvingasetoftypicalproblemsselectedfromliteraturehavedemonstratedtheextremeimportanceofthesemodificationsinmakingNocedal&Overton’soriginalmethonpractical.Furthermore,theseresultsshowthattheimprovedalgoritnmsareverycompetitiveincomparisonwithsomehighlypraisedsequentialquadraticprogrammingmethods.