Iterativetechniquesforsolvingoptimalcontrolsystemsgovernedbyparabolicvariationalinequalitiesarepresented.Thetechniquesweusearebasedonlinearfiniteelementsmethodtoapproximatethestateequationsandnonlinearconjugategradientmethodstosolvethediscreteoptimalcontrolproblem.Convergenceresultsandnumericalexperimentsarepresented.