Derive logitboost using the logistic loss function
Originally, Logitboost was derived by Friedman, Hastie, and Tibshirani (paper) -- their algorithm internally used a numerical procedure, via Newtons method to solve a regression problem.  

Later, Collins, Schapire, and Singer (paper) found an equivalent formulation, with a single-line modification from AdaBoost, setting 
$$D(i) \propto \frac{1}{1+e^{y_i f_{t-1}(x_i)}}.$$

Schapire has a nice summary of boosting here, which also discusses Logitboost.