We present a general boosting method extending functional gradient boosting to optimize complex loss functions that are encountered in many machine learning problems. Our approach is based on optimization of quadratic upper bounds of the loss functions which allows us to present a rigorous convergence analysis of the algorithm. More importantly, this general framework enables us to use a standard regression base learner such as decision trees for fitting any loss function. We illustrate an application of the proposed method in learning ranking functions for Web search by combining both preference data and labeled data for training. We present experimental results for Web search using data from a commercial search engine that show significant improvements of our proposed methods over some existing methods.