M.Phil.-Ph.D. Programme : Area I: Operations Research

 

SEEM 5320 Markov Decision Process   
SEEM 5350 Numerical Optimization
SEEM 5380 Optimization Methods for High-Dimensional Statistics
SEEM 5410 Optimal Control
SEEM 5510 System Simulation 
ENGG 5501 Foundations of Optimization (SEEM5520 Optimization I)
SEEM 5580 Advanced Stochastic Models 
SEEM 5650 Integer Programming
SEEM 5660 Conic Optimization and Applications
SEEM 5690 Queueing Systems

 

 


ENGG5501 Foundations of Optimization (SEEM5520 Optimization I)

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 theory, and basics of optimization algorithms.  Applications from different fields, such as computational economics and finance, combinatorial optimization, and signal and image processing, will be used to complement the theoretical developments. No prior optimization background is required for this class. However, students should have a workable knowledge in multivariable calculus, basic concepts of analysis, linear algebra and matrix theory.

SEEM 5320 Markov Decision Process
   
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 finite-stage models and then discuss infinite-stage models under both discounted return and average return criteria. Basic structural properties of models and computational methods will be introduced and explored. Various applications in supply chain management and other areas will be discussed.
 

SEEM 5350 Numerical Optimization
 
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 method of multipliers, coordinate descent method, and stochastic / randomized algorithms. Applications of these optimization methods for solving problems in contemporary applications arising from big data analytics, machine learning, statistics, signal processing etc. will also be discussed.

SEEM 5380 Optimization Methods for High-Dimensional Statistics

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 on the theory of structured regularizers for high-dimensional statistics and the design and analysis of statistically and computationally efficient optimization algorithms. Applications in various areas of science and engineering, such as machine learning, signal processing, and statistics, will also be discussed. Students are expected to have taken ENGG 5501 or equivalent.

SEEM 5410 Optimal Control

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 of optimality, Hamilton-Jacobi-Bellman equation, and verification theorem. Linear quadratic control: Riccati equation and linear matrix inequality. Introduction to numerical methods of solving optimal control problems.

SEEM 5510 System Simulation

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, logistics and service systems.

 

SEEM 5580 Advanced Stochastic Models

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.

SEEM 5650 Integer Programming

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. Solution methods covers partial enumeration methods, dynamic programming methods, branch and bound methods, cutting plane methods, convergent Lagrangian dual methods, convexification methods and global descent methods. These methods can be respectively applied to solve separable/non-separable and convex/non-convex integer programming problems, including nonlinear knapsack problems, quadratic integer programming, and zero-one polynomial integer programming. The course also discusses various applications of integer programming in engineering, management and finance.

SEEM5660 Conic Optimization and Applications

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 then be placed on the applications of conic optimization in engineering.

SEEM5690 Queueing Systems

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. And some applications of queueing theory in supply chain and service, operations management will be discussed.