APP MTH 4114 - Optimisation - Honours

North Terrace Campus - Semester 1 - 2016

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.

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Course Details

Course Code	APP MTH 4114
Course	Optimisation - Honours
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 hours per week
Available for Study Abroad and Exchange
Prerequisites	MATHS 1012
Assumed Knowledge	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
Assessment	Ongoing assessment 30%, exam 70%

Course Staff

Course Coordinator: Dr Sarthok Sircar

Course Timetable

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

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.
6. Demonstrate the ability to work in a group applying the theory developed in this course.

University Graduate Attributes

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

University Graduate Attribute	Course Learning Outcome(s)
Deep discipline knowledge informed and infused by cutting edge research, scaffolded throughout their program of studies acquired from personal interaction with research active educators, from year 1 accredited or validated against national or international standards (for relevant programs)	1,2,3,4
Critical thinking and problem solving steeped in research methods and rigor based on empirical evidence and the scientific approach to knowledge development demonstrated through appropriate and relevant assessment	1,3,4,5,6
Teamwork and communication skills developed from, with, and via the SGDE honed through assessment and practice throughout the program of studies encouraged and valued in all aspects of learning	5,6
Career and leadership readiness technology savvy professional and, where relevant, fully accredited forward thinking and well informed tested and validated by work based experiences	1,5,6
Intercultural and ethical competency adept at operating in other cultures comfortable with different nationalities and social contexts able to determine and contribute to desirable social outcomes demonstrated by study abroad or with an understanding of indigenous knowledges	5,6
Self-awareness and emotional intelligence a capacity for self-reflection and a willingness to engage in self-appraisal open to objective and constructive feedback from supervisors and peers able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate	6

Learning Resources

Required 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.

Recordings of lectures will also be available on MyUni following each lecture, for those who are unable to attend due to other commitments and for revision purposes.

Please don't hesitate to email the lecturer should anything be missing.

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.

Workload

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

Lecture Schedule
Week 1	Single variable 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.

Tutorial Schedule
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

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

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

Course Grading

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

M11 (Honours Mark Scheme)
Grade	Grade reflects following criteria for allocation of grade	Reported on Official Transcript
Fail	A mark between 1-49	F
Third Class	A mark between 50-59	3
Second Class Div B	A mark between 60-69	2B
Second Class Div A	A mark between 70-79	2A
First Class	A mark between 80-100	1
Result Pending	An interim result	RP
Continuing	Continuing	CN

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.
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