Inthispaper,arecursivequadraticprogrammingalgorithmisproposedandstudied.ThelinesearchfunctionsusedaxeHan'snondifferentiablepenaltyfunctionswithasecondoederpenaltyterm.InordertoavoidmaratoseffectFukushima'smixeddirectionisusedasthedirectionoflinesearch.Finally,weprovetheglobalconvergenceandthelocalsecondorderconvergenceofthealgorithm.