简介：Thispaperstudiesafamilyofthelocalconvergenceoftheimprovedsecantmethodsforsolvingthenonlinearequalityconstrainedoptimizationsubjecttoboundsonvariables.TheHessianoftheLagrangianisapproximatedusingtheDFPortheBFGSsecantupdates.Theimprovedsecantmethodsareusedtogenerateasearchdirection.Combiningwithasuitablestepsize,eachiterateswitchestotrialstepofstrictinteriorfeasibility.WhentheHessianisonlypositivedefiniteinanaffinenullsubspace,oneshowsthatthealgorithmsgeneratethesequencesconvergingq-linearlyandtwo-stepq-superlinearly.Furthermore,undersomesuitableassumptions,somesequencesgeneratedbythealgorithmsconvergelocallyone-stepq-superlinearly.Finally,somenumericalresultsarepresentedtoillustratetheeffectivenessoftheproposedalgorithms.