Title: New Frontiers in Primal-Dual Algorithms for Large-Scale Convex Optimization Levent Tuncel Abstract: As the availability of big data sets and the interest in solving much larger scale convex optimization problems increased in the last twenty years, the first-order algorithms came back to the forefront. We will focus on modelling and algorithms which utilize duality in a significant way and connect first-order algorithms to second-order algorithms in a natural way. We will start with a general discussion of utilization of the dual problem in modelling and algorithms for convex optimization, have a journey through variable metric methods in first-order algorithms, self-concordant barrier functions and then finally conclude with review and report of some exciting recent work on first-order and second-order primal-dual interior-point algorithms.