select2.js

/**
 * Select2
 */
$( '.pt-search' ).select2( {
  minimumInputLength: 2,
  placeholder: 'Search…',
  ajax: {
    url: 'http://somewebsite.com/wp-json/wp/v2/posts',
    dataType: 'json',
    data: function( params ) {
      var query = {
        search: params.term,
      }

      return query;
    },
    processResults: function( data ) {
      return {
        results: $.map( data, function( item ) {
          return {
            text: item.title.rendered,
            id: item.id
          }
        } )
      };
    }
  }
} );