Update 2018
You should be able to just set it using CSS like this..
.dropdown-menu {
min-width:???px;
}
This works in both Bootstrap 3 and Bootstrap 4.0.0 (demo).
A no extra CSS option in Bootstrap 4 is using the sizing utils to change the width. For example, here the w-100 (width:100%) class is used for the dropdown menu to fill the width of it's parent....
<ul class="dropdown-menu w-100">
<li><a class="nav-link" href="#">Choice1</a></li>
<li><a class="nav-link" href="#">Choice2</a></li>
<li><a class="nav-link" href="#">Choice3</a></li>
</ul>