Mathematics
Optimization, Part I
Build mathematical and intuitive understanding of convex sets, functions, and optimization problems.
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Course overview
Build mathematical and intuitive understanding of convex sets, functions, and optimization problems.
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What you will learn
This course is part I of a series of courses. It offers a rigorous introduction to convex optimization, guided by Boyd's foundational textbook. Covering the first half of Part I, it includes comprehensive lecture notes with all necessary proofs, enhancing the textbook material.
The course balances mathematical rigor with intuitive understanding, focusing on convex sets, functions, and optimization problems. It provides the basic mathematical treatment of convex set.
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Lecture syllabus
Video titles and durations as published on Arabsera. The advertised lecture total may differ from the number of video entries, which can include introductions, tutorials, and split sessions.
Video titles and durations
- Preface
- Snapshot of Optimization: Introduction(1/3)
- Snapshot of Optimization: introduction(2/3)
- Snapshot of Optimization: introduction(3/3)
- 05 Convex Sets: affines, lines, and line segments
- 06 Convex Sets: affines vs. subspaces
- 07 Convex Sets: affine hulls and affine combination
- 08 Convex Sets: basic topology of Euclidean space
- 09 Convex Sets: convex hulls
- 10 Convex Sets: cones and conic hulls
- 11 Convex Sets: hyperplanes and halfspaces
- 12 Convex Sets: properties of halfspaces
- 13 Convex Sets: Euclidean balls and ellipsoids
- 14 Convex Sets: norms, metrics, and loss (1/3)
- 15 Convex Sets: norms, metrics, and loss (2/3)
- 16 Convex Sets: norms, metrics, and loss (3/3)
- 17 Convex Sets: norm cones
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Teaching support (check your plan)
- Discussion groups
- TA-human texting for Q&A
- TA-GPT (coming soon)
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Textbook
Boyd, S., & Vandenberghe, L. (2004). Convex Optimization.
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Certificate
Awarded after passing a brief sample exam, which you may attempt multiple times.