Area I: Operations Research

In this course we will develop the basic machineries needed for formulating and analyzing various optimization problems. Topics include convex analysis, linear and conic linear programming, nonlinear programming, optimality conditions, Lagrangian duality...

This course covers the fundamental concepts and theories of stochastic dynamic programming (Markov decision processes) and aims to give the central ideas of how they are applied to model and solve various problems in different contexts. We start with...

This course is to teach students modern numerical optimization methods for large scale systems. Topics covered in this course include gradient method, subgradient method, proximal gradient method, Nesterov's acceleration technique, alternating direction...

The prevalence of high-dimensional data has motivated active research on efficient methods for tackling optimization problems that arise in statistical analysis. In this course, we will give an introduction to this exciting area of research, with emphasis...

Dynamic continuous-time systems. Examples, modelling, and classification of optimal control problems. Pontryagin's maximum principle: adjoint equation, Hamiltonian system, and sufficient condition of optimality. Bellman's dynamic programming: principle...

Principles of discrete event simulation. Random number generators. Simulation model validation. Input and output analysis. Optimization via simulation. Variance reduction techniques. Introduction of simulation packages and applications to finance,...

Poisson process. Birth-and-death process, Markov chain. Martingale. Brownian motion. Renewal and stationary processes. Stochastic integration and Ito's formula. Applications to queueing models, inventory models, and financial investment/hedging models. ...

The course discusses underlying theory and fundamental solution methodologies for linear and nonlinear integer programming. Theoretical topics include general solution concepts such as relaxation, partition and bounds, submodularity, and duality theory....

This course covers various topics in conic optimization, including Semidefinite Programming (SDP). In particular, we discuss theoretical properties of conic optimization models, and we introduce solution methods for solving such models. Emphasis will...

Elementary through advanced queueing systems will be covered in this course. Topics include birth-death queueing systems, Jackson network, M/G/1 and G/G/1 systems, and priority queues etc. Equilibrium behaviour in queueing systems will be introduced....