jQuery Simple Example

HTML

<script src="//www.addressfinder.co.nz/assets/v2/widget.js"></script>
<select id="options">
</select>

CSS

body {
  padding: 5px;
}

label {
  font-weight: bold;
}

input[type=text] {
  width: 20em
}

p {
  margin: 1em 0 0;
}

JavaScript

$(document).ready(function() {
  $('#options').append('<optgroup label="category1"></optgroup>');
  $('#options').append('<optgroup label="category2"></optgroup>');

  var opt1 = new Option("test1", 1);
  var opt2 = new Option("test2", 2);

  $('#options optgroup[label=category1]').append(opt1);
  $('#options optgroup[label=category2]').append(opt1);
  $('#options optgroup[label=category1]').append(opt2);
});