It is known that Abraham was strong spiritually and physically. He won the war of the four kings. He was afraid of nothing but G-d. It is also known that Abraham tried to ask for mercy and tried to convince G-d not to destroy Sodom. Why didn't Abraham try to convince Sodom people to repent and regret for what they did. There could have been even a minor chance that the people change their behavior and Sodom could have been saved. Only after failing to convince them he could ask G-d for mercy? In addition, why didn't he ask G-d to give him chance to try to convince them to regret?
He did try.
It writes in the Midrash Aggadas Bereishis 25 here that Avraham specifically set up camp opposite Sodom and its surrounding cities so that he could receive those that passed by as Sodom and Amorah did not allow guests to enter the city.