This thesis aims to study the theoretical complexity and empirical performance of decomposition algorithms. We focus on linear programs with a block-angular structure. Decomposition algorithms used to be the only way to solve large-scale special structured problems, in terms of memory limit and CPU time. However, with the advances in computer technology over the past few decades, many large-sca...

Probabilistic Latent Semantic Analysis (PLSA) is a popular technique to analyze non-negative data where multinomial distributions underlying every data vector are expressed as linear combinations of a set of basis distributions. These learned basis distributions that characterize the dataset lie on the standard simplex and themselves represent corners of a simplex within which all data approxim...