Salomon did not ask for spousal support and asked that it not be awarded to Anderson.
A phone message left for Anderson's publicist was not immediately returned Friday.
Salomon is known for making a sex videotape with then-girlfriend Paris Hilton and was previously married to actress Shannen Doherty for nine months.
He and Anderson were married Oct. 6 in Las Vegas and separated Dec. 13.
Anderson, 40, was previously married to singer Kid Rock and Motley Crue drummer Tommy Lee.