Why was portugal desperately trying to find a sea route to asia in the late 1400's?

The passages through the Mediterranean for reaching the Indian Ocean were occupied by the Arabs, and they were requesting large amounts of money or goods for passing through, and also the waters were very insecure because of the pirates. So Portugal was trying to find a way around Africa to reach the Indian Ocean and thus India, so that it can continue with trade of the goods from the Asian continent and keep its wealth and power on the global scene. 

Ummm they were radical