Year
2021
Units
4.5
Contact
3 x 50-minute lectures weekly
1 x 50-minute tutorial weekly
Prerequisites
1 MATH2701 - Principles of Analysis
2 MATH2702 - Linear Algebra and Differential Equations
3 ENGR2711 - Engineering Mathematics
4a Admission into MEB-Master of Engineering (Biomedical)
4c Admission into MEE-Master of Engineering (Electronics)
4d Admission into HBSC-Bachelor of Science (Honours)
4e Admission into HBIT-Bachelor of Information Technology (Honours)
4f Admission into MSCMT-Master of Science (Mathematics)
Must Satisfy: ((1 and 2) or (3) or ((4 or 4a or 4b or 4c or 4d or 4e or 4f)))
Enrolment not permitted
1 of MATH3703, MATH4707 has been successfully completed
Assumed knowledge
Students undertaking the one year honours programs should check to make sure they have the appropriate background from their undergraduate degree/s.
Topic description

This topic includes: Formulation of optimization problems (objective functions and constraints, existence of an optimum); Elements of convex analysis (convex sets and functions, separation theorems); Necessary and sufficient optimality conditions (including Karush-Kuhn-Tacker theorem and convex duality results);Linear programming and elements of game theory; Sensitivity and perturbation analysis Steepest decent method, Newton's method and Conjugate gradient methods in solving unconstrained problems; Penalty and barrier methods in solving constrained problems.

Educational aims

This topic aims to provide:

• An understanding of main concepts of convex analysis
• An understanding of necessary and sufficient optimality conditions
• An understanding of the role of duality in optimization theory
• An understanding of linear programming and some concepts of the game theory
• An understanding of the a role the sensitivity analysis in optimisation problems
• An introduction to numerical methods for optimization problems
Expected learning outcomes
On completion of this topic you will be expected to be able to:

1. Understand the main concepts of optimisation theory and some concepts of game theory
2. Use Lagrange multipliers to solve nonlinear optimization problems
3. Write down and apply Karush-Kuhn-Tucker conditions for constrained nonlinear optimisation problems
4. Understand the importance of convexity in nonlinear optimization problems
5. Understand and be able to apply numerical optimization techniques