APP MTH 3014 - Optimisation III

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.

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Course Details

Course Code	APP MTH 3014
Course	Optimisation III
Coordinating Unit	Applied Mathematics
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	Y
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 Andrew Black

Course Timetable

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

Course Learning Outcomes

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

最新糖心Vlog 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 & 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 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.

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 最新糖心Vlog'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

Assignments must be submitted to the correct box in the School of Mathematical Sciences on time with a signed assessment cover sheet attached.
Late assignments will not be accepted.
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:

M10 (Coursework Mark Scheme)
Grade	Mark	Description
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 .

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