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ACM41030

Academic Year 2024/2025

Optimization Algorithms (ACM41030)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Assoc Professor Lennon Ó Náraigh
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module introduces students to the theory of optimization, a key tool in modern Applied Mathematics, Operations Research, and Machine Learning. Students will study in depth the key concepts in continuous optimization - both unconstrained, constrained, and global.

About this Module

Learning Outcomes:

On completion of this module, students should be able to:

1. Formulate standard optimization techniques in continuous optimization, understand the convergence criteria, and implement these methods from scratch;
2. Implement the same methods using standard software packages, understand when these methods will work well and when they won’t;
3. Understand the first-order necessary conditions for optimality in constrained optimization, be able to solve simple problems by hand;
4. Prove the Karush-Kuhn-Tucker conditions;
5. Formulate the Dual Problem in constrained optimization;
5. Understand the need for global optimization, implement a simulated-annealing algorithm.

Indicative Module Content:

Topics covered: Steepest-Descent and Newton-type methods, including analysis of convergence, Trust-region methods, including the construction of solutions of the constrained sub-problem; Numerical implementations of standard optimization methods. Constrained Optimization with equality and inequality constraints, examples motivating the introduction of the Lagrange Multiplier Technique. Necessary first-order optimality conditions, including a derivation of the Karush-Kuhn-Tucker conditions. Farkas’s Lemma and the Separating Hyperplane Theorem. Formulation of the Dual Problem in Constrained Optimization. Introduction to Global Optimization, to include a discussion on Simulated Annealing.

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24

Autonomous Student Learning

40

Lectures

36

Total

100


Approaches to Teaching and Learning:
Lectures, tutorials, problem class, coding sessions. Opportunities for students to assess their own progress through study of model answers to exercises, as well as problem-solving and coding.

Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Class test - held after midterm break Week 10 Standard conversion grade scale 40% No
50
No
Exam (In-person): One-hour final exam End of trimester
Duration:
1 hr(s)
Standard conversion grade scale 40% No
50
No

Carry forward of passed components
No
 

Resit In Terminal Exam
Summer Yes - 1 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Self-assessment activities

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26 Thurs 15:00 - 16:50
Spring Lecture Offering 1 Week(s) - 29, 30, 31, 32, 33 Thurs 15:00 - 16:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26 Tues 09:00 - 09:50
Spring Lecture Offering 1 Week(s) - 29, 30, 31, 32, 33 Tues 09:00 - 09:50