unisa logo
books-library-folders

Area/Catalogue
MATH 3009

graduate-cap

Course Level
Undergraduate

globe-earth-geography

Offered Externally
No

diploma-certificate-graduate-degree

Course ID
013173

pie-chart-graph

Unit Value
4.5

compass

University-wide elective course
Yes

calendar-2
Timetable/s
First Semester
(Study Period 2)
Course owner

Course owner
School of Information Technology and Mathematical Sciences

Course aim

Introduce students to basic concepts and methodologies for solving differentiable optimization problems, provide tools for them to produce a model, analyse it mathematically, and write a computer code that actually solves the model using standard (MATLAB) and cutting edge (CVX) computer software.

Course content

Preliminary concepts and definitions from Linear Algebra, Analysis and topology, Optimality conditions for Unconstrained Optimization: Global and local optima, first order optimality conditions, second order optimality conditions. Conditions for existence of solutions. The quadratic case. Least squares problem. The gradient method, scaled gradient method, Gauss-Newton Method. Convergence analysis of gradient methods. Newton's method, damped Newton method. Hybrid Gradient-Newton. Convex sets and its topological properties. Convex functions. Continuity and differentiability of Convex functions. Convex optimisation: Linear programming, convex quadratic problems. Examples of use of CVX software. Optimality for continuously differentiable problems over a convex constraint set. The KKT conditions. Application of KKT conditions: Constrained Least squares. Second order optimality conditions for inequality constrained problems.

Textbook(s)

Beck, Amir 2014, Introduction to Nonlinear Optimization, MOS-SIAM Series on Optimization

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number Course Name
MATH 2014 Linear Programming and Networks

Corequisite(s)

Nil

Teaching method

Component Duration
INTERNAL, MAWSON LAKES
Lecture 2 hours x 13 weeks
Tutorial 2 hour x 13 weeks

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.


Assessment

Task Length Weighting Duration
INTERNAL, MAWSON LAKES
Continuous assessment N/A 10% N/A
Problem solving exercise 1125 words 15% N/A
Problem solving exercise 1125 word equivalent 15% N/A
Examination 2000 words equivalent 60% 3 hours

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
How to determine your Commonwealth Supported course fee. (Opens new window)

Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the Division offering the course. To determine the cost of this course, go to:
How to determine the relevant non award tuition fee. (Opens new window)

Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation

Course Coordinators

School of Information Technology and Mathematical

Degrees this course is offered in

Checking your eligibility