MATH7707 Optimisation

2019

4.5

3 x 50-minute lectures weekly
1 x 50-minute tutorial weekly

1 MATH2701 - Principles of Analysis
2 MATH2702 - Linear Algebra and Differential Equations
3 ENGR2711 - Engineering Mathematics
4 Admission into GDPEB-Graduate Diploma in Engineering (Biomedical)
4a Admission into MEB-Master of Engineering (Biomedical)
4b Admission into GDPEE-Graduate Diploma in Engineering (Electronics)
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)))

1 of MATH3703, MATH4707 has been successfully completed

Students undertaking the one year honours programs should check to make sure they have the appropriate background from their undergraduate degree/s.

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.

This topic provides:

1. An understanding of main concepts of convex analysis
2. An understanding of necessary and sufficient optimality conditions
3. An understanding of the role of duality in optimization theory
4. An understanding of linear programming and some concepts of the game theory
5. An understanding of the a role the sensitivity analysis in optimisation problems
6. An introduction to numerical methods for optimization problems

At the completion of this topic, students are 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