Basic Mathematical Optimisation

Synopsis

MTH355 Basic Mathematical Optimisation will provide undergraduates with an understanding of the common algorithms used in linear 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 simplex method and integer programming whilst only assuming a knowledge of basic linear algebra. Additionally, the course will teach students how such algorithms are implemented using the software Gurobi.

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

Topics

LU Decomposition
Matrix Iterative Methods
Formulation of a Linear Programming Model
The Simplex Method
Dual Form of a Linear Programming Problem
Sensitivity Analysis
Parametric Linear Programming
Branch and Bound Method
Either/or and 0-1 Variable Models
The Barrier Method
Goal Programming Problems involving Multiple Goals
Maximising Minima and Minimising Maxima

Learning Outcome

Formulate linear optimisation problems into mathematical and graphical linear models
Solve linear optimisation modelling problems using the simplex method
Analyse linear optimization problems with the two-phase simplex solution technique
Apply the LU decomposition technique and the conditions of convergence for linear sets of equations
Employ the branch and bound method to solve integer programming and 0-1 variable models
Compute the optimum solution of a large linear programming model

Part-time Programmes / CET Courses

Singapore University of Social Sciences

Basic Mathematical Optimisation