EDIT
This is the most optimized solution I could find using AMPScript - albeit part of it is done in SSJS, but that part greatly reduces the code weight and optimizes the speed of the script.
As I was unsure which triggers you wanted to pause or restart, I filtered based on just 'currently active'.
%%[
/************************************
Retrieve Request - list of all Triggered Sends
*************************************/
SET @rr = CreateObject("RetrieveRequest")
SetObjectProperty(@rr, "ObjectType", "TriggeredSendDefinition")
AddObjectArrayItem(@rr,"Properties","CustomerKey")
AddObjectArrayItem(@rr,"Properties","Name")
AddObjectArrayItem(@rr,"Properties","TriggeredSendStatus")
/* Invoke the Retrieve Request API */
SET @tsd = InvokeRetrieve(@rr, @Status, @RequestID)
/*******************************************
FOR loop - to iterate and update all Active Triggers
*******************************************/
FOR @c = RowCount(@tsd) DOWNTO 1 DO
SET @row = Row(@tsd ,@c)
SET @TSDName = Field(@row ,'Name')
SET @TSDKey = Field(@row ,'CustomerKey')
SET @TSDStatus = Field(@row, 'TriggeredSendStatus')
IF @TSDStatus == "Active" THEN
]%%
<script runat="server">
Platform.Load("core","1");
var tsdName = Variable.GetValue("@TSDName");
var tsd = TriggeredSend.Init(tsdName);
var pause = tsd.Pause();
var publish = tsd.Publish();
var start = tsd.Start();
</script>
%%[
ENDIF
NEXT @c
]%%
I had the same sort of issue and it took a large chunk of my life to solve.
Reference this question/answer for more info on my exact issue: SOAP API to 'publish' a TriggeredSendDefinition?
As I am assuming you want to do a pause, publish and run - See below for API calls which will do a full restart on the triggered email interaction.
You just need to do the requests via the AMPScript API functions.
See below for sample SOAP envelopes to accomplish this:
Pause
<!--***pause***-->
<soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:wsse="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-secext-1.0.xsd" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<soap:Header>
<wsse:Security soap:mustUnderstand="1">
<wsse:UsernameToken wsu:Id="UsernameToken-452336374" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<wsse:Username>USERNAME</wsse:Username>
<wsse:Password Type="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-username-token-profile-1.0#PasswordText">PASSWORD</wsse:Password>
</wsse:UsernameToken>
</wsse:Security>
</soap:Header>
<soap:Body>
<UpdateRequest xmlns="http://exacttarget.com/wsdl/partnerAPI">
<Objects xsi:type="TriggeredSendDefinition">
<!-- This section here is only necessary if you are targeting a Welcome Email within a Business Unit -->
<Client>
<ID>YOUR_MID</ID>
</Client>
<!--END-->
<CustomerKey>TriggeredSend-customer-key-goes-here</CustomerKey>
<TriggeredSendStatus>Inactive</TriggeredSendStatus>
</Objects>
</UpdateRequest>
</soap:Body>
</soap:Envelope>
Publish
<!--***publish***-->
<soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:wsse="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-secext-1.0.xsd" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<soap:Header>
<wsse:Security soap:mustUnderstand="1">
<wsse:UsernameToken wsu:Id="UsernameToken-452336374" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<wsse:Username>MC_USERNAME</wsse:Username>
<wsse:Password Type="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-username-token-profile-1.0#PasswordText">PASSWORD</wsse:Password>
</wsse:UsernameToken>
</wsse:Security>
</soap:Header>
<soap:Body>
<UpdateRequest xmlns="http://exacttarget.com/wsdl/partnerAPI">
<Objects xsi:type="TriggeredSendDefinition">
<!-- This section here is only necessary if you are targeting a Welcome Email within a Business Unit -->
<Client>
<ID>YOUR_MID</ID>
</Client>
<!--END-->
<CustomerKey>TriggeredSend-customer-key-goes-here</CustomerKey>
<RefreshContent>true</RefreshContent>
</Objects>
</UpdateRequest>
</soap:Body>
</soap:Envelope>
Restart
<!--***restart***-->
<soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:wsse="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-secext-1.0.xsd" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<soap:Header>
<wsse:Security soap:mustUnderstand="1">
<wsse:UsernameToken wsu:Id="UsernameToken-452336374" xmlns:wsu="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-wssecurity-utility-1.0.xsd">
<wsse:Username>USERNAME</wsse:Username>
<wsse:Password Type="http://docs.oasis-open.org/wss/2004/01/oasis-200401-wss-username-token-profile-1.0#PasswordText">PASSWORD</wsse:Password>
</wsse:UsernameToken>
</wsse:Security>
</soap:Header>
<soap:Body>
<UpdateRequest xmlns="http://exacttarget.com/wsdl/partnerAPI">
<Objects xsi:type="TriggeredSendDefinition">
<!-- This section here is only necessary if you are targeting a Welcome Email within a Business Unit -->
<Client>
<ID>YOUR_MID</ID>
</Client>
<!--END-->
<CustomerKey>TriggeredSend-customer-key-goes-here</CustomerKey>
<TriggeredSendStatus>Active</TriggeredSendStatus>
</Objects>
</UpdateRequest>
</soap:Body>
</soap:Envelope>