In web search, mutual influences between documents have been studied from the perspective of search result diversification. But the methods in web search is not directly applicable to e-commerce search because of their differences. And little research has been done on the mutual influences between items in e-commerce search. We propose a global optimization framework for mutual influence aware ranking in e-commerce search. Our framework directly optimizes the Gross Merchandise Volume (GMV) for ranking, and decomposes ranking into two tasks. The first task is mutual influence aware purchase probability estimation. We propose a global feature extension method to incorporate mutual influences into the features of an item. We also use Recurrent Neural Network (RNN) to capture influences related to ranking orders in purchase probability estimation. The second task is to find the best ranking order based on the purchase probability estimations. We treat the second task as a sequence generation problem and solved it using the beam search algorithm. We performed online A/B test on a large e-commerce search engine. The results show that our method brings a 5% increase in GMV for the search engine over a strong baseline.