简介:Thebilevelprogrammingisappliedtosolvehierarchicalintelligencecontrolproblemsinsuchfieldsasindustry,agriculture,transportation,military,andsoon.Thispaperpresentsaquadraticobjectivepenaltyfunctionwithtwopenaltyparametersforinequalityconstrainedbilevelprogramming.Undersomeconditions,theoptimalsolutiontothebilevelprogrammingdefinedbythequadraticobjectivepenaltyfunctionisprovedtobeanoptimalsolutiontotheoriginalbilevelprogramming.Moreover,basedonthequadraticobjectivepenaltyfunction,analgorithmisdevelopedtofindanoptimalsolutiontotheoriginalbilevelprogramming,anditsconvergenceprovedundersomeconditions.Furthermore,undertheassumptionofconvexityatlowerlevelproblems,aquadraticobjectivepenaltyfunctionwithoutlowerlevelproblemsisdefinedandisprovedequaltotheoriginalbilevelprogramming.
简介:Thispaperconsiderstheconvergenceratesfornonparametricestimatorsoftheerrordistributioninsemi-parametricregressionmodels.Byestablishingsomegenerallawsoftheiteratedlogarithm,itshowsthattheratesofconvergenceofeithertheempiricaldistributionorasmoothedversionoftheempiricaldistributionfunctionmatchesexactlytheratesobtainedforanindependentsamplefromtheerrordistribution.