1. A method for triggering optimization of a traffic engineering (TE) label switched path (LSP) that spans multiple domains of a computer network from a head-end node of a local domain to a tail-end node of a remote domain, the method comprising: detecting, at an event path computation element (PCE), an event in a remote domain (“event domain”); notifying, as a notification from the event PCE, one or more other PCEs for other domains of the event in the event domain; receiving the notification at the one or more other PCEs; and flooding, from the one or more other PCEs, the notification to one or more label switched routers (LSRs) in respective other domains of the one or more other PCEs, thereby triggering an optimization request for one or more TE-LSPs from the one or more LSRs.