MATH412-24S1 (C) Semester One 2024

Optimization

15 points

Details:
Start Date: Monday, 19 February 2024
End Date: Sunday, 23 June 2024
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 3 March 2024
  • Without academic penalty (including no fee refund): Sunday, 12 May 2024

Description

Techniques for optimising smooth functions both with and without constraints present.

Course Information:
Mathematical optimization is an important subject that has applications to many areas in science, data science, commerce and engineering. This course introduces some of the fundamental concepts, including describing what an optimization problem is, understanding what is meant by a solution, and introducing several of the foundational algorithms that can be used to tackle optimization problems. Emphasis is placed on algorithms, and understanding both how and why they work.

Topics Covered:
This course focuses on the minimization of smooth functions of several variables, in both the unconstrained and constrained cases. Topics may be chosen from the following list: Gradient Descent; Newton’s method; quasi-Newton methods; Conjugate Gradients; Augmented Lagrangian methods; Interior point methods; Trust region methods; Convexity; Positive Definiteness; Derivative approximations.

Learning Outcomes:
At the end of the course, students will:

• be familiar with the foundational algorithms for optimization;
• understand why, when and how these algorithms work;
• have observed computational aspects of the algorithms via software;
• have had the opportunity to learn problem solving skills both as part of a team and as an individual;
• have developed written and oral communications skills, emphasizing the ability to explain what the mathematics means.

Prerequisites

Subject to approval of the Head of School.

Restrictions

Timetable 2024

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 09:00 - 10:00 Jack Erskine 240
19 Feb - 31 Mar
22 Apr - 2 Jun
Lecture B
Activity Day Time Location Weeks
01 Wednesday 13:00 - 14:00 E12
19 Feb - 31 Mar
22 Apr - 2 Jun
Lecture C
Activity Day Time Location Weeks
01 Thursday 10:00 - 11:00 Jack Erskine 240
19 Feb - 31 Mar
22 Apr - 2 Jun

Course Coordinator

Rachael Tappenden

Textbooks / Resources

Recommended Reading

Fletcher, R; Practical methods of optimization ; 2nd ed.; Wiley, 1987.

Gill, Murray and Wright; Practical Optimisation ; Academic Press, 1981.

Nocedal, Jorge. , Wright, Stephen J; Numerical optimization ; 2nd ed; Springer, 2006.

Indicative Fees

Domestic fee $1,074.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH412 Occurrences

  • MATH412-24S1 (C) Semester One 2024