Check if date is in the past without submitting form

All you need to do is convert the string produced by the <input> into a Date using the Date constructor new Date("2014-06-12")

 function checkDate() {
   var selectedText = document.getElementById('datepicker').value;
   var selectedDate = new Date(selectedText);
   var now = new Date();
   if (selectedDate < now) {
    alert("Date must be in the future");
   }
 }
<input id="datepicker" onchange="checkDate()" required class="datepicker-input" type="date" data-date-format="yyyy-mm-dd" >