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This module will provide you with a sound foundation in the application of the many tools and techniques of management science. You are expected to learn the tools and the applications of modelling, optimization, computing and programming in solving practical problems drawn from many functional areas (operations, finance, marketing, and human resources, etc.) in different organizations (industry, finance, public sector, etc.).

This module will provide you with a sound foundation in the application of the many tools and techniques of management science. You are expected to learn the tools and the applications of modelling, optimization, computing and programming in solving practical problems drawn from many functional areas (operations, finance, marketing, and human resources, etc.) in different organizations (industry, finance, public sector, etc.).

This module will provide you with a sound foundation in the application of the many tools and techniques of management science. You are expected to learn the tools and the applications of modelling, optimization, computing and programming in solving practical problems drawn from many functional areas (operations, finance, marketing, and human resources, etc.) in different organizations (industry, finance, public sector, etc.).

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

This module is about the fundamentals of algorithms solving continuous optimisation problems, which involve minimising functions of multiple real-valued variables, possibly subject to restrictions, constraints, and nondifferentiable regularisations on the values that the variables may take. We focus (not exclusively) on convex optimisation, where the choice of topics is motivated by relevance to machine learning and data science.

The module has a two-part syllabus.

Part 1 covers the theoretical foundation of optimisation: convex analysis. Topics include the notion of convexity, subdifferential, optimality conditions and properties of various formulations of continuous optimisation problems.

Part 2 focuses on methods for solving optimisation problems. Topics include various gradient descent methods, higher-order methods, coordinate descent, randomisation, and heuristics.


[Module focus] This module is on structural continuous nonlinear optimisation in the real Euclidean space. This module is not about linear programming, combinatorial optimisation nor PDE-constrained optimisation.


[Prerequisites] A good knowledge of linear algebra and (differential) calculus is required for this module. Exposure to numerical analysis and vector calculus is helpful but not required; the applications will be kept basic and simple. Students will write scripts in MATLAB/Python, so familiarity with programming is required.


[Who should enrol] This module is expected to be beneficial to anyone who uses or will uses optimisation in machine learning and related work. More specifically, people from the following fields: machine learning, signal and image processing, communications, bioinformatics, control, robotics, computer graphics, computer vision, operation research, scientific computing, computational mathematics, and finance.

Optimisation under uncertainty concerns the modelling and solution of decision-making problems in which some input data are not known with certainty at the time decisions must be made. Such uncertainty is inherent in most real-world systems and arises in applications including energy systems, logistics, transportation, scheduling, healthcare, finance, and machine learning.

This module introduces the principal mathematical frameworks for optimisation under uncertainty and real-world examples using the mathematical frameworks. Students will study stochastic programming and robust optimisation. Students will learn how uncertainty can be represented mathematically and how these representations influence both modelling choices and solution approaches. The module also briefly highlights how these frameworks interact with modern data-driven methods and emerging computational technologies such as AI and quantum computing.

The course develops both theoretical foundations and practical methodologies. Core topics include two-stage, multi-stage and multi-horizon stochastic programming, risk-sensitive optimisation, dynamic decision-making models. Attention is given to scalable solution techniques, such as decomposition algorithms and value function approximation methods, that enable large-scale problems to be solved efficiently. Where appropriate, links to recent developments in areas such as machine learning and quantum computing are discussed.

The module integrates analytical development with computational implementation. Through lectures and interactive workshops, students will formulate and implement optimisation models motivated by real-world applications. By the end of the module, students will be able to model uncertainty rigorously and apply advanced optimisation tools to support robust and informed decision-making in complex problems, preparing them to competently apply optimisation under uncertainty methodologies in their future careers.