"put forth the idea" is correct and usable in written English.
You can use it to introduce a suggestion or proposal in a formal context. For example: "At the meeting, I put forth the idea of forming a committee to explore new strategies for marketing our product."
Several designers put forth the idea of longer midcalf skirts (like Marc Jacobs, left of the limo).
In an article titled "Joey, a Mechanical Boy," published in Scientific American, in 1959, Bettelheim put forth the idea that autism was a rational response of children who, dealing with a deficit of maternal emotion, reëngineered themselves as machines.
On Tuesday night, The Wall Street Journal reported that senior Genting executives put forth the idea for the convention center at a fund-raiser in October at the Westchester estate of Barry Gosin, a commercial property broker.
In their recent book Nudge, Richard Thaler and Cass Sunstein put forth the idea that choice architecture, or the design of environments in order to influence decisions, is pervasive and unavoidable and can lead to both good and bad choices.
The administration first put forth the idea a year ago, when John F. Kelly, then secretary of the Department of Homeland Security, said he was considering separating parents from their children as a deterrent to illegal immigration.
These discoveries were made in a series of experiments that built on the work of Gustav Becking, a German musicologist who first put forth the idea of composers' pulses in 1928.
Contributors put forth the ideas that few regulatory instruments are actually purely market-based, or purely prescriptive, and that both approaches can be systematically undermined by insufficiently careful design and by failures of monitoring and enforcement.
But just as he tells us "This Is Not a Pipe," Mr. Demand quietly puts forth the idea of landscape as the ultimate "treachery of image".
The film, echoing the scientific consensus, puts forth the idea that repetitive subconcussive blows are thought to be the main cause of C.T.E.
Ultimately, the exhibition puts forth the idea that, when inserted into a carefully constructed display, art becomes a useful tool for appropriating the past and controlling the present, or even the future.
Dr. McWhiney (pronounced like "whinny") was also a respected judge of fiddling contests, but his major contribution was in putting forth the idea that Southerners descend from the wild Celtic tribes of Scotland, Ireland and Wales.
