AKindofdirectmethodsispresentedforthesolutionofoptimalcontrolproblemswithstateconstraints.Thesemethodsaresequentialquadraticprogrammingmethods.AteveryiterationaquadraticprogrammingwhichisobtainedbyquadraticapproximationtoLagrangianfunctionandLinearapproximationstoconstraintsissolvedtogetasearchdirectionforameritfunction.ThemeritfunctionisformulatedbyaugmentingtheLagrangianfunetionwithapenaltyterm.Alinesearchiscarriedoutalongthesearchdirectiontodetermineasteplengthsuchthatthemeritfunctionisdecreased.Themethodspresentedinthispaperincludecontinuoussequentialquadraticprogrammingmethodsanddiscreatesequentialquadradeprogrammingmethods.