The search can be invoked dynamically upon grid load. Just set search to true and the criteria.
The data of search can be saved in session to be used later when user come to this page.
<?php 
require_once '../../../../php/demo/tabs.php';
?>
<!DOCTYPE html>
<html>
  <head>
    <title>jqGrid PHP Demo</title>
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/jquery-ui.css" />
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/trirand/ui.jqgrid.css" />
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/ui.multiselect.css" />
    <style type="text">
        html, body {
        margin: 0;            /* Remove body margin/padding */
        padding: 0;
        overflow: hidden;    /* Remove scroll bars on browser window */
        font-size: 75%;
        }
        
    </style>
    <script src="../../../../js/jquery.min.js" type="text/javascript"></script>
    <script src="../../../../js/trirand/i18n/grid.locale-en.js" type="text/javascript"></script>
         <script src="../../../../js/trirand/jquery.jqGrid.min.js" type="text/javascript"></script> <script type="text/javascript">         
    $.jgrid.no_legacy_api = true;
    $.jgrid.useJSON = true;
    $.jgrid.defaults.width = "700";
    </script>
     
    <script src="../../../../js/jquery-ui.min.js" type="text/javascript"></script>
  </head>
  <body>
      <div>
          <?php
ini_set('display_errors',0);
include ("grid.php");
?>
      </div>
      <br/>
<?php tabs(array("grid.php"));?>
   </body>
</html>
grid.php.
<?php
require_once '../../jq-config.php';
// include the jqGrid Class
require_once ABSPATH."php/PHPSuito/jqGrid.php";
// include the driver class
require_once ABSPATH."php/PHPSuito/DBdrivers/jqGridPdo.php";
// Connection to the server
$conn = new PDO(DB_DSN,DB_USER,DB_PASSWORD);
// Tell the db that we use utf-8
$conn->query("SET NAMES utf8");
// Create the jqGrid instance
$grid = new jqGridRender($conn);
// Write the SQL Query
$grid->SelectCommand = 'SELECT OrderID, OrderDate, CustomerID, ShipName, Freight FROM orders';
// Set output format to json
$grid->dataType = 'json';
// Let the grid create the model
$grid->setColModel();
// Set the url from where we obtain the data
$grid->setUrl('grid.php');
if(!isset($_SESSION)) {
    session_start();
}
if( jqGridUtils::GetParam('_search') == 'true') {
    $searchstring = jqGridUtils::GetParam("filters");
    $searchobject = jqGridUtils::decode($searchstring);
    if (isset($searchobject['rules']) && count($searchobject['rules'])>0 ) {
        foreach($searchobject['rules'] as $key=>$val) {
            if(isset($val['field'])) {
                $field = $val['field'];
                $_SESSION[$field]= $val['data'];
            }                
        }
    }
}
$myorder = isset($_SESSION['OrderID'])? $_SESSION['OrderID'] : "10255";



// initialsearch 
$sarr = <<< FFF
{ "groupOp":"AND",
    "rules":[
      {"field":"OrderID","op":"lt","data":"$myorder"}
     ]
}
FFF;
// other fields can be added here with
//{"field":"Freight","op":"gt","data":"0"}

// Set some grid options
$grid->setGridOptions(array(
    "rowNum"=>10,
    "rowList"=>array(10,20,30),
    "sortname"=>"OrderID",
    // set the initila search upon loading
    "search"=>true, 
    // setr criteria
    "postData"=>array( "filters"=> $sarr )
));
//toolbarfilter sttings
$grid->setColProperty("OrderID", array(
    // the value set in filters is 10255
    "searchoptions"=>array("defaultValue"=>"$myorder", "sopt"=>array("lt"))
    )
);


// Change some property of the field(s)
$grid->setColProperty("OrderDate", array(
    "formatter"=>"date",
    "formatoptions"=>array("srcformat"=>"Y-m-d H:i:s","newformat"=>"m/d/Y")
    )
);
$grid->setColProperty("ShipName", array("width"=>"200"));
// Enable navigator
$grid->navigator = true;
$grid->toolbarfilter = true;
// Enable search
// By default we have multiple search enabled
$grid->setNavOptions('navigator', array("excel"=>false,"add"=>false,"edit"=>false,"del"=>false,"view"=>false));
// In order to enable the more complex search we should set multipleGroup option
// Also we need show query roo
$grid->setNavOptions('search', array(
    "multipleGroup"=>true,
    "showQuery"=>true
));
// Enjoy
$grid->renderGrid('#grid','#pager',true, null, null, true,true);
$conn = null;
?>