简介：Thebilevelprogrammingisappliedtosolvehierarchicalintelligencecontrolproblemsinsuchfieldsasindustry,agriculture,transportation,military,andsoon.Thispaperpresentsaquadraticobjectivepenaltyfunctionwithtwopenaltyparametersforinequalityconstrainedbilevelprogramming.Undersomeconditions,theoptimalsolutiontothebilevelprogrammingdefinedbythequadraticobjectivepenaltyfunctionisprovedtobeanoptimalsolutiontotheoriginalbilevelprogramming.Moreover,basedonthequadraticobjectivepenaltyfunction,analgorithmisdevelopedtofindanoptimalsolutiontotheoriginalbilevelprogramming,anditsconvergenceprovedundersomeconditions.Furthermore,undertheassumptionofconvexityatlowerlevelproblems,aquadraticobjectivepenaltyfunctionwithoutlowerlevelproblemsisdefinedandisprovedequaltotheoriginalbilevelprogramming.

简介：Thispaperconsiderstheconvergenceratesfornonparametricestimatorsoftheerrordistributioninsemi-parametricregressionmodels.Byestablishingsomegenerallawsoftheiteratedlogarithm,itshowsthattheratesofconvergenceofeithertheempiricaldistributionorasmoothedversionoftheempiricaldistributionfunctionmatchesexactlytheratesobtainedforanindependentsamplefromtheerrordistribution.