# Course - Continuous Optimisation HT26

> Source: https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/ · Updated: 2026-05-13 · Tags: uni, course

- [Course webpage](https://courses.maths.ox.ac.uk/course/view.php?id=6141)
- Lecture notes (old):
	- [1a, Problems and solutions. Optimality conditions for unconstrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119000/mod_folder/content/0/C62_Lecture1a_2024.pdf)
	- [1b, Problems and solutions. Optimality conditions for unconstrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119000/mod_folder/content/0/C62_Lecture1b_2024.pdf)
	- [2, Problems and solutions. Optimality conditions for unconstrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119000/mod_folder/content/0/C62_Lecture2_2024.pdf)
	- [3a, Methods for unconstrained optimisation. Linesearch algorithms](https://courses.maths.ox.ac.uk/pluginfile.php/119001/mod_folder/content/0/C62_Lecture3a_2024.pdf)
	- [3b, Methods for unconstrained optimisation. Linesearch algorithms](https://courses.maths.ox.ac.uk/pluginfile.php/119001/mod_folder/content/0/C62_Lecture3b_2024.pdf)
	- [4, Methods for unconstrained optimisation. Linesearch algorithms](https://courses.maths.ox.ac.uk/pluginfile.php/119001/mod_folder/content/0/C62_Lecture4_2024.pdf)
	- [5, Steepest descent methods](https://courses.maths.ox.ac.uk/pluginfile.php/119002/mod_folder/content/0/C62_Lecture5_2024.pdf)
	- [6a, Newton's method for unconstrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119003/mod_folder/content/0/C62_Lecture6a_2024.pdf)
	- [6b, Newton's method for unconstrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119003/mod_folder/content/0/C62_Lecture6b_2024.pdf)
	- [7, Quasi-Newton methods. Nonlinear least-squares and Gauss-Newton methods](https://courses.maths.ox.ac.uk/pluginfile.php/119004/mod_folder/content/0/C62_Lecture7_2024.pdf)
	- [8, Trust region methods](https://courses.maths.ox.ac.uk/pluginfile.php/119005/mod_folder/content/0/C62_Lecture8.pdf)
	- [9a, Trust region methods](https://courses.maths.ox.ac.uk/pluginfile.php/119005/mod_folder/content/0/C62_Lecture9a.pdf)
	- [9b, Trust region methods](https://courses.maths.ox.ac.uk/pluginfile.php/119005/mod_folder/content/0/C62_Lecture9b.pdf)
	- [10, Optimality conditions for constrained problems](https://courses.maths.ox.ac.uk/pluginfile.php/119006/mod_folder/content/0/C62_Lecture10and11.pdf)
	- [11, Optimality conditions for constrained problems](https://courses.maths.ox.ac.uk/pluginfile.php/119006/mod_folder/content/0/C62_Lecture10and11.pdf)
	- [12, Penalty methods for constrained optimisation](https://courses.maths.ox.ac.uk/pluginfile.php/119007/mod_folder/content/0/C62_Lecture12.pdf)
	- [13, Augmented Lagrangian methods](https://courses.maths.ox.ac.uk/pluginfile.php/119008/mod_folder/content/0/C62_Lecture13.pdf)
	- [14, Interior point methods for inequality constrained optimisation problems](https://courses.maths.ox.ac.uk/pluginfile.php/119009/mod_folder/content/0/C62_Lecture14and15.pdf)
	- [15, Interior point methods for inequality constrained optimisation problems](https://courses.maths.ox.ac.uk/pluginfile.php/119009/mod_folder/content/0/C62_Lecture14and15.pdf)
	- [16, SQP methods for constrained optimisation (nonexaminable)](https://courses.maths.ox.ac.uk/pluginfile.php/119010/mod_folder/content/0/C62_Lecture16.pdf)
- Additional resources:
	- [Proof of convergence of trust region methods (nonexaminable)](https://courses.maths.ox.ac.uk/pluginfile.php/119011/mod_folder/content/0/Lecture9_CompleteProof_Trust_Region.pdf)
	- [Proof of second-order optimality conditions for constrained problems (nonexaminable)](https://courses.maths.ox.ac.uk/pluginfile.php/119011/mod_folder/content/0/Lecture11_ProofTheorem19.pdf)
	- [Mathematical background](https://courses.maths.ox.ac.uk/pluginfile.php/119012/mod_folder/content/0/C62_MathematicalBackground.pdf)
	- [Other useful resources](https://courses.maths.ox.ac.uk/pluginfile.php/119012/mod_folder/content/0/C62_Resources.pdf)
	- [Prof. Yuji Nakatsukasa's notes on Taylor's theorem](https://courses.maths.ox.ac.uk/pluginfile.php/119012/mod_folder/content/0/Taylor.pdf)
	- [Prof. Raphael Hauser's continuous optimisation notes](https://courses.maths.ox.ac.uk/pluginfile.php/119012/mod_folder/content/0/Taylor.pdf)
- Lecture recordings:
	- [2024-2025](https://ox.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?embedded=1#folderID=%22295247b3-8dad-4310-a15e-b1b900999cc2%22)
	- [2025-2026](https://ox.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?embedded=1#folderID=%22d90fd11d-68bb-44de-bd4d-b31a00798fac%22)
- Other courses this term: [Courses HT26](https://ollybritton.com/notes/uni/part-c/ht26/)
- My notes here are based primarily on the slides above, written by [Prof. Coralia Cartis](https://www.maths.ox.ac.uk/people/coralia.cartis).
- See also: [Course - Optimisation for Data Science HT25](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/)

### Notes
- [Notes - Continuous Optimisation HT26, Overview of results and methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/overview-of-results-and-methods/)

- [Notes - Continuous Optimisation HT26, Optimisation terminology](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/optimisation-terminology/)
- [Notes - Continuous Optimisation HT26, Taylor's theorem](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/taylors-theorem/)
- [Notes - Continuous Optimisation HT26, Unconstrained optimality conditions](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/unconstrained-optimality-conditions/)
- [Notes - Continuous Optimisation HT26, Unconstrained optimality conditions for convex problems](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/unconstrained-optimality-conditions-for-convex-problems/)
- [Notes - Continuous Optimisation HT26, Linesearch methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/linesearch-methods/)
- [Notes - Continuous Optimisation HT26, Steepest descent](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/steepest-descent/)
- [Notes - Continuous Optimisation HT26, Newton's method](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/newtons-method/)
- [Notes - Continuous Optimisation HT26, Quasi-Newton methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/quasi-newton-methods/)
- [Notes - Continuous Optimisation HT26, Least-squares](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/least-squares/)
- [Notes - Continuous Optimisation HT26, Trust-region methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/trust-region-methods/)
- [Notes - Continuous Optimisation HT26, Constrained optimisation problems](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/constrained-optimisation-problems/)
- [Notes - Continuous Optimisation HT26, KKT conditions](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/kkt-conditions/)
- [Notes - Continuous Optimisation HT26, Constrained optimality conditions for convex problems](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/constrained-optimality-conditions-for-convex-problems/)
- [Notes - Continuous Optimisation HT26, Penalty methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/penalty-methods/)
- [Notes - Continuous Optimisation HT26, Augmented Lagrangian methods](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/augmented-lagrangian-methods/)
- [Notes - Continuous Optimisation HT26, Inequality constrained optimisation problems](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/inequality-constrained-optimisation-problems/)

- [Notes - Continuous Optimisation HT26, Useful miscellany](https://ollybritton.com/notes/uni/part-c/ht26/continuous-optimisation/notes/useful-miscellany/)

### Related notes
There is a significant amount of overlap with the Part B [Course - Optimisation for Data Science HT25](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/):

- [Notes - Optimisation for Data Science HT25, Overview of results](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/overview-of-results/)
- [Notes - Optimisation for Data Science HT25, Terminology](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/terminology/)
- [Notes - Optimisation for Data Science HT25, Convexity](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/convexity/)
- [Notes - Optimisation for Data Science HT25, Steepest descent](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/steepest-descent/)
- [Notes - Optimisation for Data Science HT25, Steepest descent with inexact line search](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/steepest-descent-with-inexact-line-search/)
- [Notes - Optimisation for Data Science HT25, Misc](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/misc/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/119014/mod_assign/introattachment/0/C6.2ProblemSheet1-2024.pdf) ([solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/119014/mod_assign/introattachment/0/C62-Sheet%201-2024_SolutionsPartsAC.pdf), [additional past paper questions](https://courses.maths.ox.ac.uk/pluginfile.php/119014/mod_assign/introattachment/0/C6.2_PastPaperExercises_Sheet1.pdf)), [redacted](https://ollybritton.com/404)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/119015/mod_assign/introattachment/0/C62_ProblemSheet_2-2024.pdf) ([solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/119015/mod_assign/introattachment/0/C62_ProblemSheet_2-2024.pdf)), [redacted](https://ollybritton.com/404)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/119016/mod_assign/introattachment/0/C62_Problem_Sheet3-2024.pdf) ([solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/119016/mod_assign/introattachment/0/C6.2ProblemSheet3PartsAandC_2024.pdf)), [redacted](https://ollybritton.com/404)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/119017/mod_assign/introattachment/0/C62_Problem_Sheet4_2024.pdf) ([solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/119017/mod_assign/introattachment/0/C62_Problem_Sheet4_PartsAandC_2024.pdf)), [redacted](https://ollybritton.com/404)

- #comment

### To-Do List

#### Priority gaps from [redacted](https://ollybritton.com/404)

##### Priority 1 (correctness fixes + missing examinable lectures)

##### Priority 2 (medium fixes + clean lecture-grounded gaps)

##### Priority 3 (typos, smaller gaps, structural decisions)

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