My notes for when I took this course in Fall 2025, taught by Somayeh Sojoudi.

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Please submit any errors you might find in the errata, thank you!

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Phoenix Wilson

Shout out to George Ma for some of the illustrations used here!

Course by Week

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The notes on the linear algebra module are not comprehensive.

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Week Topics
1 Standard Form, Minima, Feasibility
2 Affine Sets, Projections
3 Hyperplanes
4 Spectral Theorem, Sign Definite Matrices, Multivariate Taylor Expansions, Hessians
5 Singular Value Decomposition, Moore-Penrose Pseudoinverse, Matrix Norms, Low Rank Factorization
6 Low-Rank Approximation, PCA, Sensitivity Analysis
7 Ellipsoids, Least Squares Perturbation, Elementary Topology
8 Convex Sets, Convex Functions
9 Convex Optimization, Coercive Functions
10 Linear Programs, Superlinear Programs, Convex Relaxation
11 Integer Programs, Compressed Sensing, Lasso
12 Slater’s Condition, Karush-Kuhn-Tucker, Lagrangian
13 Duality
14 Infeasibility Certificates, Constraint Elimination, Sensitivity Parameters
15 Matrix Optimization, Iterative Methods

Standard Form, Minima, Feasibility

Affine Sets, Projections

Hyperplanes

Spectral Theorem, Sign Definite Matrices, Multivariate Taylor Expansions, Hessians

Singular Value Decomposition, Moore-Penrose Pseudoinverse, Matrix Norms, Low Rank Factorization

Low-Rank Approximation, PCA, Sensitivity Analysis

Ellipsoids, Least Squares Perturbation, Elementary Topology

Convex Sets, Convex Functions

Convex Optimization, Coercive Functions

Linear Programs, Superlinear Programs, Convex Relaxation

Integer Programs, Compressed Sensing, Lasso