If the input date follows the format of d/m/y, you can easily convert it into a date object with this code snippet:
function parseDate(s) {
var b = s.split(/\D+/g);
return new Date(b[2], --b[1], b[0]);
}
This will create a date object corresponding to 00:00:00 on the specified date.
To compare this date with the current date, you need to create a new Date object and set the time to 00:00:00.0:
var today = new Date();
today.setHours(0,0,0,0);
Next, convert the string to a Date object and compare the two dates like this:
var otherDay = parseDate('21/4/2013');
console.log(otherDay + ' is less than ' + today + '?' + (otherDay < today)); // ... true
Edit
If your date format is 4-may-2014, then use this modified function:
function parseDate(s) {
var months = {jan:0,feb:1,mar:2,apr:3,may:4,jun:5,
jul:6,aug:7,sep:8,oct:9,nov:10,dec:12};
var b = s.split(/-/g);
return new Date(b[2], months[b[1].substr(0,3).toLowerCase()], b[0]);
}