php, you can use array_reduce to traverse once

$dates = ['2018-07-21','2018-08-13','2018-08-30','2018-9-02','2018-09-28','2018-11-02'];
$minSeconds = null;

$result = [];
array_reduce($dates, function($date1, $date2) use(&$minSeconds, &$result) {
    if (empty($date1)) {
        return $date2;
    }
    $date1Seconds = strtotime($date1);
    $date2Seconds = strtotime($date2);
    $seconds = $date2Seconds - $date1Seconds;
    
    if ($minSeconds === null || $seconds < $minSeconds) {
        $minSeconds = $seconds;
        $result = [$date1, $date2];
    }
    return $date2;
}, null);
print_r($result);

sorted? Then directly compare the two adjacent dates, from the beginning to the end to find out the minimum time difference on the line.

const arr=['2018-07-21','2018-08-13','2018-08-30','2018-9-02','2018-09-28','2018-11-02'];
    function toDate(str){
        const arr=str.split(/\D+/);
        arr[1]-=1;
        arr.unshift(Date);
        const d=+new (Date.bind.apply(Date,arr))();
        return d;
    }
    const timeArr=arr.map(toDate);
    let min,index;
    for(let i=0;i<timeArr.length-2;iPP){
        const dur=timeArr[i+1]-timeArr[i];
        if(min === undefined){
            min=dur;
            index=i;
        }else if(min>dur){
           min=dur;
           index=i;
        }
    }
    console.log(arr[index],arr[index+1]);

suppose your dates are sorted in order if you don't sort first

take advantage of sorting to make it easier to calculate by the way

var dtStart;
var dtEnd;
var tmDelta = -1;
['2018-07-21','2018-08-13','2018-08-30','2018-9-02','2018-09-28','2018-11-02'].sort(function($a, $b){
    var tmA = (new Date($a)).getTime();
    var tmB = (new Date($b)).getTime();

    var delta = Math.abs(tmA - tmB);
    if(tmDelta == -1 || delta > tmDelta)
    {
        tmDelta = delta;
        dtStart = $a;
        dtEnd   = $b;
    }

    return tmA - tmB;
})

console.log(dtStart, dtEnd)

I'll have a PHP

$arr=['2018-07-21','2018-08-13','2018-08-30','2018-9-02','2018-09-28','2018-11-02'];
$data = [];
for ($i = count($arr)-1 ; $i >= 0; $i--) { 
    for ($j = 0; $j < $i ; $jPP) { 
        $a = $arr[$i];
        $b = $arr[$j];
        $v = date_diff(date_create($a), date_create($b)); // 
        //  http://php.net/manual/zh/function.date-diff.php
        //  
        // $data[$a.'-'.$b] = $v->format('%a');
        $data[$v->format('%a')] = $a.'-'.$b;
    }
}
echo "
";
//$res = array_flip($data);  //
ksort($data); //
var_dump(array_shift($data)); //  string(20) "2018-9-02-2018-08-30"