NANCY BENACWASHINGTON (AP) ¿ The fare can be as simple as a cheeseburger and fries. The lunches are often pay-as-you-go affairs. Yet they are some of the most coveted invitations in town. Five times since last summer, President Obama has invited a small group of corporate CEOs in for a private lunch at the White House. The business titans gather with Obama in his private dining room just off the Oval Office, or elsewhere in the White House, to talk over global economic policy, corporate bonuses, climate change, high school dropout rates and more. There's no set agenda as the president picks the brains of some of the brightest minds in the corporate world. But Obama said the sessions have helped him think through ways to create a "smarter economy." Early on, when the economy was reeling, his conversations with corporate leaders had a "solving-the-problem-right-in-front-of-you flavor," Obama said. But now that the situation has stabilized, he's able to think through "bigger, strategic questions" with them, Obama told Business Week last month. The CEOs, for their part, get to offer perspectives from the corporate suite, and size up the president in an unrivaled setting. Lew Hay, chairman and chief executive of power producer FPL Group Inc., remembers his lunch with the president last October as a "kind of heady experience," and said the president went out of his way to put his four lunch guests at ease. "It was far easier to relax in his presence than I think any of us would have expected," Hay said in an interview, adding that Obama seemed intent on getting all he could out of the session. "Sometimes people talk to you, and they're going through the motions," Hay said. "He was deeply engaged through the entire time." The lunches are part of a broader administration effort to reach out to big business at a time when even Obama has acknowledged there's a perception that his administration has been anti-business. This is a president, after all, whose finger-wagging at "fat cat bankers" and "obscene" executive bonuses grated with corporate chieftains.