The phrase "launch a competition" is correct and usable in written English.
You can use it when referring to the act of starting or initiating a contest or competition.
Example: "We plan to launch a competition next month to encourage innovation among our employees."
Alternatives: "start a contest" or "initiate a competition."
Alternatively, you might look externally and launch a competition that asks startups to make more disruptive proposals.
Tony Cocker of E.ON said he had called on the prime minister to launch a competition investigation.
"I'm going to launch a competition for a 12,000-seat arena," he proclaimed at the NLA, to the assembled architects' glee.
The Department for Communities and Local Government has just announced it is to launch a competition to choose 12 towns to become "Portas Pilots", named after report author and retail guru Mary Portas.
"This work will support decisions later in the year on whether to proceed with the GoCo option and whether to launch a competition for the private sector management company to run the organisation.
Ed Miliband had pledged to launch a competition investigation, and shadow chancellor Ed Balls said: "In the next parliament we need to see at least two new challenger banks and a market-share test to ensure the market stays competitive for the long term".
Mr Straw also said the Government was "launching a competition" to provide a new prison ship.
Bookninja has launched a competition to "remasculate" the authors, titles, and plots of famous books.
1.30pm Grand National day competition By popular demand we are launching a competition today.
And we launched a competition asking our supporters, the Arctic needs your imagination, what would you build to save it?
On his ITV show, he has launched a competition to find the People's Novelist with HarperCollins.
