Sort array by a date string in multidimensional array

Below is the working code as your expectation.

compare_dates = function(date1,date2){

      d1= new Date(date1[0]);
      d2= new Date(date2[0]);
      if (d1>d2) return 1;
       else if (d1<d2)  return -1;
       else return 0;
    }
    var objs = [
        ['01-Sep-2018', 'Some other Value'],
        ['20-Aug-2018', 'Some other Value'],
        ['21-Aug-2018', 'Some other Value'],
        ['22-Aug-2018', 'Some other Value'],
        ['23-Aug-2018', 'Some other Value']
    ];

    objs.sort(compare_dates);

    console.log(objs);

You can use Array.sort for this, the only complication is making the dates into something JS can parse. This can be done by replacing the - in the date with spaces, converting them to something like '20 Sep 2018' which is fine as an input to the Date constructor.

let array = [
    ['01-Sep-2018', 'Some other Value'],
    ['20-Aug-2018', 'Some other Value'],
    ['21-Aug-2018', 'Some other Value'],
    ['22-Aug-2018', 'Some other Value'],
    ['23-Aug-2018', 'Some other Value']
];
array.sort((a, b) => new Date(a[0].replace(/-/g, ' ')) - new Date(b[0].replace(/-/g, ' ')));
console.log(array);

You can do it with Array.prototype.sort and Array.prototype.map to extract the date values:

const data = [['01-Sep-2018', 'Some other Value'],['20-Aug-2018', 'Some other Value'],['21-Aug-2018', 'Some other Value'],['22-Aug-2018', 'Some other Value'],['23-Aug-2018', 'Some other Value']];

const sorted = data.sort((a,b) => {
    
    const [aD, bD] = [a,b].map(([d]) => new Date(d.replace(/-/gi,' ')))

    return aD - bD;

});

console.log(sorted);