select2 v3.x

If you have local array with options (received by ajax call), i think you should use data parameter as function returning results for select box:

var pills = [{id:0, text: "red"}, {id:1, text: "blue"}]; 

$('#selectpill').select2({
    placeholder: "Select a pill",
    data: function() { return {results: pills}; }
});

$('#uppercase').click(function() {
    $.each(pills, function(idx, val) {
        pills[idx].text = val.text.toUpperCase();
    });
});
$('#newresults').click(function() {
    pills = [{id:0, text: "white"}, {id:1, text: "black"}];
});

FIDDLE: http://jsfiddle.net/RVnfn/576/

In case if you customize select2 interface with buttons, just call updateResults (this method not allowed to call from outsite of select2 object but you can add it to allowedMethods array in select2 if you need to) method after updateting data array(pills in example).

---

select2 v4: custom data adapter

Custom data adapter with additional updateOptions (its unclear why original ArrayAdapter lacks this functionality) method can be used to dynamically update options list (all options in this example):

$.fn.select2.amd.define('select2/data/customAdapter',
    ['select2/data/array', 'select2/utils'],
    function (ArrayAdapter, Utils) {
        function CustomDataAdapter ($element, options) {
            CustomDataAdapter.__super__.constructor.call(this, $element, options);
        }
        Utils.Extend(CustomDataAdapter, ArrayAdapter);
        CustomDataAdapter.prototype.updateOptions = function (data) {
            this.$element.find('option').remove(); // remove all options
            this.addOptions(this.convertToOptions(data));
        }        
        return CustomDataAdapter;
    }
);

var customAdapter = $.fn.select2.amd.require('select2/data/customAdapter');

var sel = $('select').select2({
    dataAdapter: customAdapter,
    data: pills
});

$('#uppercase').click(function() {
    $.each(pills, function(idx, val) {
        pills[idx].text = val.text.toUpperCase();
    });
    sel.data('select2').dataAdapter.updateOptions(pills);
});

FIDDLE: https://jsfiddle.net/xu48n36c/1/

---

select2 v4: ajax transport function

in v4 you can define custom transport method that can work with local data array (thx @Caleb_Kiage for example, i’ve played with it without succes)

docs: https://select2.github.io/options.html#can-an-ajax-plugin-other-than-jqueryajax-be-used

Select2 uses the transport method defined in ajax.transport to send
requests to your API. By default, this transport method is jQuery.ajax
but this can be changed.

$('select').select2({
    ajax: {
        transport: function(params, success, failure) {
            var items = pills;
            // fitering if params.data.q available
            if (params.data && params.data.q) {
                items = items.filter(function(item) {
                    return new RegExp(params.data.q).test(item.text);
                });
            }
            var promise = new Promise(function(resolve, reject) {
                resolve({results: items});
            });
            promise.then(success);
            promise.catch(failure);
        }
    }
});

BUT with this method you need to change ids of options if text of option in array changes – internal select2 dom option element list did not modified. If id of option in array stay same – previous saved option will be displayed instead of updated from array! That is not problem if array modified only by adding new items to it – ok for most common cases.

FIDDLE: https://jsfiddle.net/xu48n36c/3/