Cheesecake Factory Inc. has initiated the process for opening a new restaurant in Hawaii. The Calabasas company on Tuesday filed a building permit request with the County of Honolulu for a $4.5 million restaurant at the site of the Ka Makana Ali’i mixed-use retail destination in West Oahu, according to public record. The center opened in mid-October upon completing the first of two development phases and is the third-largest regional mall in Hawaii. If the request is approved, the Oahu restaurant will be Cheesecake’s second location in the state. Its first Hawaii outpost opened in 2003 at the Royal Hawaiian Center in Honolulu. The company operates 185 restaurants under its Cheesecake Factory, Grand Lux Cafe and Rocksugar Pan Asian Kitchen brands and employs approximately 35,000 workers. Cheesecake (CAKE) stock fell 87 cents, or 1.4 percent, on Wednesday to close at $61.31 on the Nasdaq.