Simplest Answer

array.sort(function(a,b){
  // Turn your strings into dates, and then subtract them
  // to get a value that is either negative, positive, or zero.
  return new Date(b.date) - new Date(a.date);
});

More Generic Answer

array.sort(function(o1,o2){
  if (sort_o1_before_o2)    return -1;
  else if(sort_o1_after_o2) return  1;
  else                      return  0;
});

Or more tersely:

array.sort(function(o1,o2){
  return sort_o1_before_o2 ? -1 : sort_o1_after_o2 ? 1 : 0;
});

Generic, Powerful Answer

Define a custom non-enumerable sortBy function using a Schwartzian transform on all arrays :

(function(){
  if (typeof Object.defineProperty === 'function'){
    try{Object.defineProperty(Array.prototype,'sortBy',{value:sb}); }catch(e){}
  }
  if (!Array.prototype.sortBy) Array.prototype.sortBy = sb;

  function sb(f){
    for (var i=this.length;i;){
      var o = this[--i];
      this[i] = [].concat(f.call(o,o,i),o);
    }
    this.sort(function(a,b){
      for (var i=0,len=a.length;i<len;++i){
        if (a[i]!=b[i]) return a[i]<b[i]?-1:1;
      }
      return 0;
    });
    for (var i=this.length;i;){
      this[--i]=this[i][this[i].length-1];
    }
    return this;
  }
})();

Use it like so:

array.sortBy(function(o){ return o.date });

If your date is not directly comparable, make a comparable date out of it, e.g.

array.sortBy(function(o){ return new Date( o.date ) });

You can also use this to sort by multiple criteria if you return an array of values:

// Sort by date, then score (reversed), then name
array.sortBy(function(o){ return [ o.date, -o.score, o.name ] };

See http://phrogz.net/JS/Array.prototype.sortBy.js for more details.

Try using the Date.getTime() method:

public sortByDueDate(): void {
    this.myArray.sort((a: TaskItemVO, b: TaskItemVO) => {
        return a.dueDate.getTime() - b.dueDate.getTime();

    });
}

^ Above throws error with undefined date so try below:

Edit

If you want to handle undefined:

private getTime(date?: Date) {
    return date != null ? date.getTime() : 0;
}


public sortByDueDate(): void {
    this.myArray.sort((a: TaskItemVO, b: TaskItemVO) => {
        return this.getTime(a.dueDate) - this.getTime(b.dueDate);
    });
}