I see in v3 reference in mailJet's site http://dev.mailjet.com/email-api/v3/newsletter-send/ there is the following example:
curl -s -X POST \
--user "$MJ_APIKEY_PUBLIC:$MJ_APIKEY_PRIVATE" \
https://api.mailjet.com/v3/REST/newsletter/:id/send
but I can't find in all your code any example how it should be done with mailjet Java API https://github.com/mailjet/mailjet-apiv3-java?
According to the response of mailJet's support their Java Wrapper is not completed and majority of REST API they still don't cover. So if you are going to use mailjet-apiv3-java library you should be ready to implement by yourself some REST commands.