V rabote dany razlichnye opredeleniya subdifferentsiala pervogo, vtorogo i vysshego poryadkov, opredeleny lipshitsevye funktsii v tochke i izuchen ryad ikh svoystv. Poluchen ryad teorem o tochnom shtrafe, a takzhe naydeny neobkhodimye i dostatochnye usloviya vysshego poryadka pri nalichii ogranicheniy. V rabote izucheny takzhe ekstremal"naya zadacha dlya differentsial"nykh vklyucheniy. Klyuchevye slova: subdifferentsial, ekstremal"naya zadacha, mnogoznachnoe otobrazhenie, differentsial"noe vklyuchenie, normal"nyy integrant.