American Airlines has kicked off its $1.6-billion overhaul at Los Angeles International Airport, one of a series of pricey LAX upgrades that will add gates, bigger bathrooms and floor-to-ceiling windows at the carrier’s terminals. A groundbreaking ceremony Wednesday attended by Los Angeles Mayor Eric Garcetti and American Airlines Chief Executive Doug Parker initiated a 10-year construction project that represents the single largest airport investment in the history of the Fort Worth carrier.