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 the remote domain (“event domain”) that provides an additional link or additional bandwidth on an existing link for use with TE-LSPs; 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; determining, at the one or more other PCEs, whether any TE-LSPs originating in respective other domains of the one or more other PCEs would benefit from optimization based on the event in the event domain; and provided that at least one TE-LSP in each of the respective other domains of the one or more other PCEs would benefit, flooding, from the one or more other PCEs, the notification to one or more label switched routers (LSRs) in the 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, the optimization request to cause use of at least a portion of the additional link or bandwidth by the one or more TE-LSPs.