Advanced Mathematical Optimisation

Synopsis

MTH356 will provide undergraduates with an understanding of the common algorithms used in nonlinear optimisation. The topics covered are of central importance for many applications in data science and data analytics. The course gives a comprehensive introduction to the gradient method and that of constrained nonlinear programming. Additionally, the course covers how such algorithms are implemented using the software Baron. MTH356 will be paired with MTH355 so that students upon the completion of both courses receive a better comprehension of the contents in the specialist field of Optimisation.

Level: 3
Credit Units: 5
Presentation Pattern: EVERY JULY

Topics

Basic Iterative Schemes to Solve Systems of Nonlinear Equations
Convergence of Simple Iterative Methods of Nonlinear Equations
Grid Search Method
Golden Section Search
Alternating Variable Search Method for a Minimum
Steepest Descent Search Method for a Minimum
Conjugate Direction Methods
Stopping Criteria for the Iteration Methods
Equality Constrained Models
Newton-Lagrange Method
Conversion to Equality Constraints
Conditions for a Local Minimiser

Learning Outcome

Solve single nonlinear equations and systems of nonlinear equations.
Interpret the convexity of sets and functions.
Determine the existence and uniqueness of solutions to a given nonlinear programming problem.
Show the necessary and sufficient optimality conditions for a given nonlinear programming problem.
Apply various numerical algorithms to solve nonlinear programming problems.
Analyse the convergence of various gradient-based iterative methods.

Part-time Programmes / CET Courses

Singapore University of Social Sciences

Advanced Mathematical Optimisation