Indeed the Portuguese built up their eastern empire with an astonishing speed. They used their naval power to gain control over the Indian Ocean by occupying a number of strategic points and to divert the stream of merchandise - particularly spices - from Asia to Portugal via the Cape of Good Hope by blockading the entrance to the Red Sea and the Gulf,
Because the Ottoman Empire had a grasp over the Mediterranean Portugal had to occupy the Cape of Africa. For the Portuguese it was another way to trade with India and china without the burden of Ottomans Tariffs.