Ali Ibn Abi talib was sent to Yemen (Mudhij or Madhij) to preach the message of Islam. To do missionary work. Some have claimed that Ali (ra) sole mission was to reduce and or force non-Muslims to convert to Islam.
However, this is not true, given the fact that the reports (below) tell us that he was sent to preach to them about the religion of Islam. In-fact, Prophet Muhammed (p) clearly told Ali not to fight them, unless they fought and attacked the Muslims first.
“THE EXPEDITION OF ALI B. ABI TALIB TO YEMEN
They said: The Messenger of God sent Ali during Ramadan in the year ten AH. The Messenger of God commanded him to camp in Quba, so Ali camped there until his companions arrived. At that time the Messenger of God offered Ali a turban, which he folded in four and fixed on the top of his spear, for a banner and handed it to him. He said, ‘This is the banner.’ He draped a turban, rolled thrice, on Ali, placing an arm length between his hand and a span length on his back, saying, ‘This is the turban!’ He said: Usama B. Zayd related to me from his father from Ata b. Yasar from Abu Rafi, who said: When the Messenger of God faced him, he said, ‘Depart and do not turn back.’ Ali said, ‘O Messenger of God, what shall I do?’ The Prophet said, ‘When you alight in their courtyard, do not fight them until they fight you; if they attack you, do not fight them until they kill one of you. If they kill one of you, do not fight them or blame them, but show them patience. Say to them, ‘Will you say that there is but one God?’ And if they say, ‘Yes,’ say, ‘Will you pray?’ And if they say ‘Yes,’ say, ‘Will you take from your property and give charity to your poor?’ And if they say ‘Yes,’ do not desire anything else. By God, may God guide a man by your hand…'” 
Kitab al-Tabaqat al-Kabir – Ibn sa’d:
“They (narrators) said: The Apostle of Allah, sent Ali to al-Yaman and prepared a banner for him. He put the turban on his head with his own hand, and said: Go and do not pay attention to anything. When you reach there, do not fight them (Yamanites) until they fight you. He set out with three hundred horsemen, and it was the first cavalry detachment that ever reached that region, which was the territory of Madhhij. …” 
“The farewell Hajj was the first and only hajj performed by the Messenger of God. It was during the Hajj that he bid the farewell to his followers (Ummah). At the time, Ali was not in Mecca. The Noble Messenger had sent him to Yemen to invite the people of Yemen to Islam. One by one, Ali visited people in their homes to convey the message. His only desire was to plant the love of God in their hearts. As soon as he heard about the Prophet’s farewell Hajj, he left Yemen for Mecca. …” 
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 The Life of Muhammad: Al-Waqidi’s Kitab Al-Maghazi [Translator: Rizwi Faizer], page 508
 Kitab al-Tabaqat al-Kabir, by ibn sa’d volume 2, page 209
 Leading Companions Of The Prophet: Ali Ibn Abi Talib: The Hero of Chivalry [2013, Tughra books], By Resit Haylamaz, page 73