I'd suggest passing an anonymous function to the sort() method:

var dates = ['10-Jan-2013','12-Dec-2013','1-Sep-2013','15-Sep-2013'],
    orderedDates = dates.sort(function(a,b){
        return Date.parse(a) > Date.parse(b);
    });

console.log(orderedDates); // ["10-Jan-2013", "1-Sep-2013", "15-Sep-2013", "12-Dec-2013"]

var dates = ['10-Jan-2013', '12-Dec-2013', '1-Sep-2013', '15-Sep-2013'],
  orderedDates = dates.sort(function(a, b) {
    return Date.parse(a) > Date.parse(b);
  });

console.log(orderedDates);

JS Fiddle demo.

Note the use of an array ['10-Jan-2013','12-Dec-2013','1-Sep-2013','15-Sep-2013'] of quoted date-strings.

The above will give you an array of dates, listed from earliest to latest; if you want only the earliest, then use orderedDates[0].

A revised approach, to show only the earliest date – as requested in the question – is the following:

var dates = ['10-Jan-2013', '12-Dec-2013', '1-Sep-2013', '15-Sep-2013'],
    earliest = dates.reduce(function (pre, cur) {
        return Date.parse(pre) > Date.parse(cur) ? cur : pre;
    });

console.log(earliest); // 10-Jan-2013

var dates = ['10-Jan-2013', '12-Dec-2013', '1-Sep-2013', '15-Sep-2013'],
  earliest = dates.reduce(function(pre, cur) {
    return Date.parse(pre) > Date.parse(cur) ? cur : pre;
  });

console.log(earliest);

JS Fiddle demo.

References:

• Date.parse().
• Array.prototype.reduce().
• Array.prototype.sort().

Sometimes the most basic approach is the best:

var dates = ["09/09/2009", "16/07/2010", "29/01/2001"];
var min = dates[0];
for(var i = 1; i < dates.length; i++) {
  if (fDate(dates[i]) < fDate(min))
    min = dates[i];
}

alert(min);

// create a proper Date object from the string
function fDate(s) {
  var d = new Date();
  s = s.split('/');
  d.setFullYear(s[2]);
  d.setMonth(s[1]);
  d.setDate(s[0]);
  return d;
}

The code I wrote for you above converts each string into a Date object, and then finds the minimum (the earliest date) from them. No string hacks, just straightforward date comparison. It returns the original string from the array.

At first you should split your string, then sort your array and pick the first element from the sorted array:

let str = '2019-12-31T23:45:00.000-03:00/2020-01-01T10:30:00.000+06:00,2020-01-01T07:15:00.000+07:00/2019-12-31T16:00:00.000-10:00';
let dates = str.split(/[\,/]+/);

let sortedDates = dates.sort((a,b) =>{
    a = a.substring(0, a.lastIndexOf('.'));
    b = b.substring(0, b.lastIndexOf('.'));
    return new Date(a) - new Date(b);
});
console.log(`earliest date is ${sortedDates[0]}`);

I've used substring function to get date to be parsed by .parse() method.

Code is tested with IE,FF,Chrome and works properly:

var dates=[];
dates.push(new Date("2011/06/25"))
dates.push(new Date("2011/06/26"))
dates.push(new Date("2011/06/27"))
dates.push(new Date("2011/06/28"))
var maxDate=new Date(Math.max.apply(null,dates));
var minDate=new Date(Math.min.apply(null,dates));

A clean way to do it would be to convert each date to a Date() and take the max

ES6:

new Date(Math.max(...a.map(e => new Date(e.MeasureDate))));

JS:

new Date(Math.max.apply(null, a.map(function(e) {
  return new Date(e.MeasureDate);
})));

where a is the array of objects.

What this does is map each of the objects in the array to a date created with the value of MeasureDate. This mapped array is then applied to the Math.max function to get the latest date and the result is converted to a date.

By mapping the string dates to JS Date objects, you end up using a solution like Min/Max of dates in an array?

--

A less clean solution would be to simply map the objects to the value of MeasureDate and sort the array of strings. This only works because of the particular date format you are using.

a.map(function(e) { return e.MeasureDate; }).sort().reverse()[0]

If performance is a concern, you may want to reduce the array to get the maximum instead of using sort and reverse.

As @Barmar said in comments:

Sort the array in reverse by date. Then use find() to find the first element before effData.

1. sort date in descending order
2. find the nearest to the date effDate

const items = [{ item: 'Two', date: '2018-01-01' }, { item: 'Three', date: '2019-01-01' }, { item: 'One', date: '2022-01-01' }, { item: 'Four', date: '2021-01-01' }, ];
const getItem = (effDate) => {
  //1.
  let itemsSorted = items.slice().sort((a, b) => Date.parse(b.date) - Date.parse(a.date))
  //2. 
  return itemsSorted.find(item => Date.parse(item.date) < Date.parse(effDate));
};
console.log(getItem('2020-08-22'));

I found _.min is reliable on moment instances. The following works:

    var dates = _.map([date1,date2],function(date){return moment(date)});
    var start = _.min(dates);    

nevermind.

You can use Array.reduce() and on each iteration compare the dates and take the oldest:

const creationDate = ['Wed Feb 13 21:14:55 GMT 2019','Wed Feb 13 21:19:42 GMT 2019','Wed Feb 13 21:28:29 GMT 2019','Wed Feb 13 21:31:04 GMT 2019'];

const oldest = creationDate.reduce((c, n) => 
  Date.parse(n) < Date.parse(c) ? n : c
);

console.log(oldest);