You can always format a date by extracting the parts and combine them using string functions in desired order:

function formatDate(date) {
  let datePart = [
    date.getMonth() + 1,
    date.getDate(),
    date.getFullYear()
  ].map((n, i) => n.toString().padStart(i === 2 ? 4 : 2, "0")).join("/");
  let timePart = [
    date.getHours(),
    date.getMinutes(),
    date.getSeconds()
  ].map((n, i) => n.toString().padStart(2, "0")).join(":");
  return datePart + " " + timePart;
}

let date = new Date();
console.log("%o => %s", date, formatDate(date));

Use below function in fiddle

     <a href="https://jsfiddle.net/pareshmutha1900/mbcmf0k4/">Link</a>

     var dateFormat = function () {
            var    token = /d{1,4}|m{1,4}|yy(?:yy)?|([HhMsTt])\1?|[LloSZ]|"[^"]*"|'[^']*'/g,
                timezone = /\b(?:[PMCEA][SDP]T|(?:Pacific|Mountain|Central|Eastern|Atlantic) (?:Standard|Daylight|Prevailing) Time|(?:GMT|UTC)(?:[-+]\d{4})?)\b/g,
                timezoneClip = /[^-+\dA-Z]/g,
                pad = function (val, len) {
                    val = String(val);
                    len = len || 2;
                    while (val.length < len) val = "0" + val;
                    return val;
                };

            // Regexes and supporting functions are cached through closure
            return function (date, mask, utc) {
                var dF = dateFormat;

                // You can't provide utc if you skip other args (use the "UTC:" mask prefix)
                if (arguments.length == 1 && Object.prototype.toString.call(date) == "[object String]" && !/\d/.test(date)) {
                    mask = date;
                    date = undefined;
                }

                // Passing date through Date applies Date.parse, if necessary
                date = date ? new Date(date) : new Date;
                if (isNaN(date)) throw SyntaxError("invalid date");

                mask = String(dF.masks[mask] || mask || dF.masks["default"]);

                // Allow setting the utc argument via the mask
                if (mask.slice(0, 4) == "UTC:") {
                    mask = mask.slice(4);
                    utc = true;
                }

                var    _ = utc ? "getUTC" : "get",
                    d = date[_ + "Date"](),
                    D = date[_ + "Day"](),
                    m = date[_ + "Month"](),
                    y = date[_ + "FullYear"](),
                    H = date[_ + "Hours"](),
                    M = date[_ + "Minutes"](),
                    s = date[_ + "Seconds"](),
                    L = date[_ + "Milliseconds"](),
                    o = utc ? 0 : date.getTimezoneOffset(),
                    flags = {
                        d:    d,
                        dd:   pad(d),
                        ddd:  dF.i18n.dayNames[D],
                        dddd: dF.i18n.dayNames[D + 7],
                        m:    m + 1,
                        mm:   pad(m + 1),
                        mmm:  dF.i18n.monthNames[m],
                        mmmm: dF.i18n.monthNames[m + 12],
                        yy:   String(y).slice(2),
                        yyyy: y,
                        h:    H % 12 || 12,
                        hh:   pad(H % 12 || 12),
                        H:    H,
                        HH:   pad(H),
                        M:    M,
                        MM:   pad(M),
                        s:    s,
                        ss:   pad(s),
                        l:    pad(L, 3),
                        L:    pad(L > 99 ? Math.round(L / 10) : L),
                        t:    H < 12 ? "a"  : "p",
                        tt:   H < 12 ? "am" : "pm",
                        T:    H < 12 ? "A"  : "P",
                        TT:   H < 12 ? "AM" : "PM",
                        Z:    utc ? "UTC" : (String(date).match(timezone) || [""]).pop().replace(timezoneClip, ""),
                        o:    (o > 0 ? "-" : "+") + pad(Math.floor(Math.abs(o) / 60) * 100 + Math.abs(o) % 60, 4),
                        S:    ["th", "st", "nd", "rd"][d % 10 > 3 ? 0 : (d % 100 - d % 10 != 10) * d % 10]
                    };

                return mask.replace(token, function ($0) {
                    return $0 in flags ? flags[0.slice(1, $0.length - 1);
                });
            };
        }();

        // Some common format strings
        dateFormat.masks = {
            "default":      "ddd mmm dd yyyy HH:MM:ss",
            shortDate:      "m/d/yy",
            mediumDate:     "mmm d, yyyy",
            longDate:       "mmmm d, yyyy",
            fullDate:       "dddd, mmmm d, yyyy",
            shortTime:      "h:MM TT",
            mediumTime:     "h:MM:ss TT",
            longTime:       "h:MM:ss TT Z",
            isoDate:        "yyyy-mm-dd",
            isoTime:        "HH:MM:ss",
            isoDateTime:    "yyyy-mm-dd'T'HH:MM:ss",
            isoUtcDateTime: "UTC:yyyy-mm-dd'T'HH:MM:ss'Z'"
        };

        // Internationalization strings
        dateFormat.i18n = {
            dayNames: [
                "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat",
                "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"
            ],
            monthNames: [
                "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec",
                "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"
            ]
        };

        // For convenience...
        Date.prototype.format = function (mask, utc) {
            return dateFormat(this, mask, utc);
        };





    today = new Date();
    var dateString = today.format("yyyy-mm-dd h:mm");
    alert(dateString);

var date_old //your old date in yyyy-mm-dd
var date = dateFormat(new Date(date_old), 'dd-mm-yyyy');

You can do:

function formatDate(date) {
    var d = new Date(date),
        month = '' + (d.getMonth() + 1),
        day = '' + d.getDate(),
        year = d.getFullYear();

    if (month.length < 2) 
        month = '0' + month;
    if (day.length < 2) 
        day = '0' + day;

    return [year, month, day].join('-');
}
 
console.log(formatDate('Sun May 11,2014'));

Usage example:

console.log(formatDate('Sun May 11,2014'));

Output:

2014-05-11

Demo on JSFiddle: http://jsfiddle.net/abdulrauf6182012/2Frm3/

Some answers don't quite solve the issue. They print the date formatted as mm/dd/yyyy but the question was regarding MM/dd/yyyy. Notice the subtle difference? MM indicates that a leading zero must pad the month if the month is a single digit, thus having it always be a double digit number.

i.e. whereas mm/dd would be 3/31, MM/dd would be 03/31.

I've created a simple function to achieve this. Notice that the same padding is applied not only to the month but also to the day of the month, which in fact makes this MM/DD/yyyy:

function getFormattedDate(date) {
  var year = date.getFullYear();

  var month = (1 + date.getMonth()).toString();
  month = month.length > 1 ? month : '0' + month;

  var day = date.getDate().toString();
  day = day.length > 1 ? day : '0' + day;
  
  return month + '/' + day + '/' + year;
}

Update for ES2017 using String.padStart(), supported by all major browsers except IE.

function getFormattedDate(date) {
    let year = date.getFullYear();
    let month = (1 + date.getMonth()).toString().padStart(2, '0');
    let day = date.getDate().toString().padStart(2, '0');
  
    return month + '/' + day + '/' + year;
}