Monash University Handbook

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Professor Andreas Ernst

Coordinator(s)

Professor Andreas Ernst
Dr Janosch Rieger

Unit guides

Second semester

Offered

Clayton

Second semester 2018 (On-campus)

Prerequisites

Students must be enrolled in the Master of Financial Mathematics or have passed: one of MTH2010, MTH2015, ENG2005 or MAT1830, and one of MTH2021, MTH2025, MTH2040 or MAT1841

Synopsis

This unit introduces some of the fundamental methods from operations research and computational mathematics for continuous optimisation problems. A range of such optimisation problems appear in economics, engineering, finance, business, data science and many other application areas. Students will receive an introduction to the mathematical theory of continuous optimisation with a focus on linear programming methods and smooth non-linear programming. This will broadly include duality theory, the simplex method for linear programming, Lagrangian relaxation methods for dealing with constraints, quadratic programming, and some methods for more general non-linear problems including iterative approximation. Students will learn to implement the computational methods efficiently, how to test their implementations for accuracy and performance, and to interpret the results. Students will work on realistic models for applications in a variety of fields. Applications may include examples of supply chain optimisation, economic modelling (including shadow prices), product mix optimisation, portfolio optimisation, parameter estimation and machine learning.

Outcomes

On completion of this unit students will be able to:

Formulate a range of operations research problems as linear programming problems, and be able to solve them computationally;
Demonstrate an understanding how the most widely used linear programming algorithms work;
Apply duality theory to prove optimality of a solution;
Interpret the solutions of optimisation problems, including analysing sensitivity of solutions;
Implement several iterative algorithms for solving constrained and unconstrained non-linear optimisation problems and understand the mathematics behind these;
Formulate and solve general non-linear programs arising in engineering, data science and other areas.