EE8231 Optimization Theory Course Project

Logistic regression and matrix factorization specifically SVD are both very popular in application areas of computational advertising and recommender system. This project basically can be divided into two parts. The first part is to test different optimization methods to solve sparse 2-class logistic regression. This is a convex non-smooth problem. Particularly, I’ll try to answer the question of ”how to handle the non-smooth part of the L1-regularizer in the objective function”. The second part is to try to solve the convex approximation of the matrix completion problem specifically SVD and extend this approximation from the L2-norm loss function to hinge/logistic loss function which would combine these two parts together. Beyond traditional SVD, SVDFeature[1] or other similar model is proposed to handle auxiliary information. This project also tries to give a convex approximation to the auxiliary information augmented family of SVD models.