Spurred by the knowledge that the convention business has become one of the biggest growth industries, major cities are committing more resources to sharply competitive campaigns aimed at capturing a bigger share of that business.

With the District's emergence as the center for national trade and professional associations, much of the competition for convention business is being waged at local hotels.

A New York-based public relations firm recently concluded: "Washington is the most important center in the country for all other American cities who are seeking a slice of the approximately $15 billion worth of trade show and meeting business being contracted for annually by the associations."

With that in mind, big city mayors, convention center managers and their public relations counsel converged on the Sheraton Washington Hotel last week with an impressive array of marketing programs.

The targets were the more than 1,200 delegates to the Joint Conference on Medical Conventions, who found themselves being buttonholed from the moment of their arrival.

In their bids to capture a medical convention, marketing officials and others representing major cities made their sales pitches at breakfast, lunch, dinner and in hospitality suites. From elaborate scale models to sophisticated multi-media programs, from handouts to business cards, the message was the same--"We want you to meet in our city."

"This is a very, very hard-sell thing," said Austin Kenny, director of the Washington Convention and Visitors Association.

What's more, said Kenny, increased competition for convention business has caused the hard-sell approach to become "a very common thing" among cities.

"We did a luncheon presentation today and all week long we had five or six people buttonholing" officials from the JCMC, said Kenny.

In addition, delegates to the conference were taken on tours of the District's convention center, which is scheduled to open this year.

One of the strongest bids in this latest round of competition last week came from Indianapolis, which is building a $70 million, 63,000-seat domed stadium and convention center.

Standing next to an elaborate, $100,000-model of the facility, Indianapolis Mayor William H. Hudnut said he expects to make that city a major competitor for convention business by the time the center is completed in 1984.

"What we're trying to illustrate here is that we have a city that is vital, alive and has a lot of momentum and is a good place to attract a lot of convention business," said Hudnut. "That's the whole part of my being here."

Hudnut, who likened himself to "Daniel in the lion's den," by bringing his campaign to Washington--a major convention city despite the lack of a major convention center--said Indianpolis is "trying to build our assets" by attracting a larger share of the business.

Indianapolis' existing convention center was the seventh largest when it was built in the early '70s. "Now it's the 40th in size, which means that a lot of people have outpaced us," Hudnut said.

In addition to its bid for a bigger slice of the convention business pie, Indianapolis has launched simultaneous campaigns to win a major league baseball franchise and a National Football League team, both of which would play in the domed stadium.

The facility is a key to downtown development and would be a gateway to a $182 million, 31-mile-long urban theme park that the state of Indiana has approved for construction along the White River.

Pointing to models of the convention center and park, Hudnut declared: "I think part of the job of a mayor is to sell your city. I'm bullish on Indianapolis and an unabashed fan but I'm also realistic.

"We recognize that we're competing with many major cities around the country for convention business."