## APP MTH 7072 - Optimisation

### North Terrace Campus - Semester 1 - 2015

Most problems in life are optimisation problems: what is the best design for a racing kayak, how do you get the best return on your investments, what is the best use of your time in swot vac, what is the shortest route across town for an emergency vehicle, what are the optimal release rates from a dam for environmental flows in a river? Mathematical formulations of such optimisation problems might contain one or many independent variables. There may or may not be constraints on those variables. There is always, though, an objective: minimise or maximise some function of the variable(s), subject to the constraints. This course will examine nonlinear mathematical formulations, and will concentrate on convex optimisation problems. Many modern optimisation methods in areas such as design of communication networks, finance, etc, rely on the classical underpinnings covered in this course. Topics covered are: One-dimensional (line) searches: direct methods, polynomial approximation, methods for differentiable functions; Theory of convex and nonconvex functions relevant to optimisation; Multivariable unconstrained optimisation, in particular, higher-order Newton's Method, steepest descent methods, conjugate gradient methods; Constrained optimisation, including Kuhn-Tucker conditions and the Gradient Projection Method.

• General Course Information
##### Course Details
Course Code APP MTH 7072 Optimisation Applied Mathematics Semester 1 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week Y MATHS 1012 Knowledge of linear programming such as would be obtained from APP MTH 2105 and basic computer programming skills such as would be obtained from COMP SCI 1012, 1101, MECH ENG 1100, 1102, 1103, 1104, 1105, C&ENVENG 1012 ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Dr Andrew Black

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
1. Understand the complexities of, and techniques for solving, nonlinear optimisation problems.
2. Apply suitable algorithms to one- or multi-dimensional optimisation problems.
3. Understand the theoretical framework underlying the techniques presented in class.
4. Implement computer code for the algorithms as studied in class and critically analyse and interpret the results.
5. Demonstrate skills in communicating mathematics orally and in writing.

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 1,4,5
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 2,4,5
Skills of a high order in interpersonal understanding, teamwork and communication. 5
A proficiency in the appropriate use of contemporary technologies. 4
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5
A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 1,4,5
An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 1,5
• Learning Resources
None.
##### Recommended Resources
Chong and Zak, An Introduction to Optimization (Wiley).
##### Online Learning
All assignments, tutorials, handouts and solutions, where appropriate, will be made available on MyUni as the course progresses.
• Learning & Teaching Activities
##### Learning & Teaching Modes
The lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Students are expected to attend all lectures, but lectures will be recorded to help with occasional absences and for revision purposes. In fortnightly tutorials students present their solutions to assigned exercises and discuss them with the lecturer and each other. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Lectures 30 90 Tutorials 6 18 Assignments 5 48 Total 156
##### Learning Activities Summary
 Week 1 Single value optimisation Introduction, Dichotomous and Golden section searches Week 2 Fibbonachi and unbounded searches Week 3 Quadratic approximation, DSC algorithm Week 4 Unconstrained multi-variable optimisation Newtons method, introduction to unconstrained problems Week 5 Convexity, theorems for minimality and descent methods Week 6 Steepest descent on quadratics Week 7 Conjugate gradient method Week 8 Constrained convex optimisation Fletcher-Reeves algorithm, introduction to constrained optimisation Week 9 Linear constraints, Lagrange multipliers, KKT conditions Week 10 Generalisations of KKT conditions, orthogonal projection Week 11 Non-convex optimisation Gradient Projection algorthm, introduction to non-convex optimisation. Week 12 Simulated Annealing methods, revision.
 Week 2 Dichotomous and Golden Section search methods Week 4 Quadratic approximation methods Week 6 1-D Newton's method and Convex functions Week 8 Steepest Descent Methods Week 10 Conjugate Gradient Methods Week 12 Non-convex methods

• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Assessment task Task type Weighting Learning outcomes Examination Summative 70% All Assignments Formative and summative 30% All
##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 Week 2 Week 3 6% Assignment 2 Week 4 Week 5 6% Assignment 3 Week 6 Week 7 6% Assignment 4 Week 8 Week 9 6% Assignment 5 Week 10 Week 11 6%
##### Submission
1. Assignments must be submitted to the correct box in the School of Mathematical Sciences on time with a signed assessment cover sheet attached.
2. Late assignments will not be accepted.
3. Assignments will be returned within two weeks to provide feedback to students.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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