This week TRW Inc. named the winner of a contest that has a prize worth more than $1 million. Although the competition attracted a good number of entrants, not everybody thinks it was such a swell idea.

TRW asked architecture firms to compete against each other for the job of designing its new world headquarters in Lyndhurst, Ohio, a Cleveland suburb. A seven-member selection committee considered 50 or so candidates and came up with four finalists, each of which submitted a plan for the building.

"All of the final eight were very good," said Jack Gearhart, who headed the committee and is in charge of the headquarters project. "It was extremely difficult to select the final four." The winner: Fujikawa Conterato Lohan & Associates in Chicago.

The practice of architects entering organized competitions to win the right to design public projects is a long-accepted exercise. But now a growing number of corporations, such as TRW, are holding competitions of their own. It's a switch from the "old days, when companies called and said, 'Would you like to do our job?'" says Timothy L. Horn, an architect with Brubaker/Brandt Inc., a Columbus, Ohio, firm that was a finalist in the TRW competition.

Some architects aren't as enthusiastic about corporate competitions as the corporations are, however. "Generally speaking, we don't like them," said a member of a leading architectural firm. That's partly because architects must invest a lot of time and money drawing up sketches and making scale models of corporate buildings without any guarantee that the client will select their work. (Clients usually fund only a small portion of an architect's expense for these sketches and models, which can range from $60,000 to $100,000.)

Mark Cameron, marketing manager of The Architects Collaborative, a Cambridge, Mass., firm, says architectural competition "are the worst way we can spend our marketing dollar" because of "the gamble we take." Still, his firm entered and won the 1973 competition to design Johns-Manville Co.'s corporate headquarters near Denver.

The risks also haven't deterred Fujikawa Conterato Lohan & Associates, which won the McDonald's Corp. headquarters competition in 1978. Melvin J. Wilson, an associate, says his firm overspent by a healthy sum the $40,000 allowance TRW gave each finalist. But he says the contract will be worth "certainly more than $1 million and probably closer to $2 million."

Beyond the expense involved, some architects consider the competitions degrading. "Companies wouldn't ask lawyers or doctors to give them a sample of their work for nothing," says Cameron of The Architects Collaborative. "When you start handing it out for free, you defeat the purpose of handling the work on a professional level."

Corporations see nothing wrong with competitions, however. TRW, for example, must submit designs of electronic and aerospace systems to government contractors when it bids competitively for space and defense work. Gearhart says TRW finds that this type of competition "enhances creativity." It also gives the winner access to the losers' designs, from which they can pick and choose ideas.

One advantage of a competition is that it gives a company more of a say in the design process. Arco Chemical Co., a division of Atlantic Richfield Co., held an architects' competition three years ago to select the firm to design its research and engineering center on a 313-acre parcel of land about 15 miles west of Philadelphia.

The Arco chemical site is surrounded by large estates and contains a wide belt of woods, a couple of meadows and several stone cottages. "We didn't buy that piece of land to have an ordinary thing put on it," says Peter A. Zambelli, an Atlantic Richfield public affairs manager and a member of the final selection committee. But, he adds, "You'd be surprised at the number of architects that wiped out the site and essentially said, 'Here's your monument to me.'"

Davis, Brody & Associates, the architect arco Chemical selected, "had the greatest sensitivity to the site," Zambelli said. Employes can look out the center's windows and enjoy a sense of daylight and a sense of vista." Davis, Brody also was a finalist in the TRW competition.

It isn't likely, however, that corporation competitions will become the standard way that companies select a designer. Although more companies are turning to them, cost is a limiting factor.

"It's easy to get a quarter- to a half-million dollars tied up in administering and holding a competition," says David O. Meeker, president of the American Institute of Architects. Consequently, he says, competitions will be restricted to major buildings of companies with "very, very substantial economic bases, and ones who want to make a strong architectural statement about their corporation."