HONOLULU — Waikiki might be one of the most famous beaches in the world, a synonym for surfing and sun-soaked vacations that draw millions of people annually. But for years, Honolulu and the State of Hawaii have been reckoning with a very uncomfortable fact: The beach is vanishing. Just below the infinity pool at the Sheraton Waikiki, an advancing shoreline claimed a walkway and set of concrete stairs, which now dangle above the water. At the Outrigger Reef hotel, ocean water laps directly against the wall of the new Monkeypod Kitchen restaurant, still under renovation.Like many places buffeted by the ocean, Waikiki has swung into action — to a point. The hotels along the beach are worth north of a billion dollars, and to preserve that investment, hotel owners and other businesses fund the Waikiki Beach Special Improvement District Association as a kind of coastline-repair department. Near the pink, 94-year-old Royal Hawaiian hotel, the association (in partnership with the state) recently built a $1.8 million groin — an L-shaped finger of rock and concrete that juts into the water and holds sand in place — in addition to widening the beach by 30 feet with 20,000 cubic yards of sand vacuumed up from the bottom of the sea. The group’s next phase of work calls for more of the same: Spending at least $50 million, much of it likely from state and perhaps federal funding, on four more groins and the construction of an entirely new beach in the area fronting the Sheraton, Outrigger Reef and Halekulani hotels.