Analysis and Optimization · Mathematics
Lagrangian, ODEs and some other concepts in optimization problems
Langrangian, KKT, ODE, Calculus of Variations, Control Theory
Follows the textbook very strictly - Further Mathematics for Economic Analysis
Review of concepts from across multiple past classes (ODEs, Linear Algebra, Calculus) to then take them a step further by applying them to optimization problems
further exploration of linear algebra and differential equations in the context of optimization
We reviewed specific topics in linear algebra, multivariable calculus, and ordinary differential equations in order to apply these techniques to optimization problems. We covered general optimization, constrained optimization, Kuhn-Tucker conditions, and calculus of variations.
In this class, Analysis and Optimization, I revisited linear algebra and calculus while learning various optimization methods to find extrema in different scenarios.
analysis and optimization, often geared towards economics
quiz in the first week, weekly psets, midterm, final
Jan 18. Overview. Linear algebra: vectors (I.1) Jan 23. Matrices, determinant (I.1). Jan 25. Linear independence, subspaces, dimension (I.2). Rank (I.3). Linear systems (I.4) Jan 30. Eigenvalues, eigenvectors (I.5). Diagonal matrices, conjugate matrices (I.6) Feb 1. Diagonalization. Spectral theorem for symmetric matrices (I.6). Quadratic forms (I.7) Feb 6. Quadratic forms (I.7). Open sets, closed sets, convergence, continuity (XIII.1) Feb 8. Differentiability, gradient (II.1) Feb 13. Convex sets, convex functions (II.2,3). Feb. 15. Quiz. Convex functions (II.3) Feb. 20. Convex functions, Jensen's inequality (II.3-4) Feb. 22. Subgradients. Taylor's formula (II.4,6) Feb. 27. Mappings, chain rule (II.9). Inverse mapping theorem (II.7) Mar. 1. Implicit function theorem (II.7). Extreme and critical points (III.1) Mar. 6. First-order conditions for convex functions. Weierstrass theorem (III.1) Mar. 8. Second-order conditions (III.2). Equality constraints: necessary conditions (III.3) Mar. 20. Equality constraints (III.3) Mar. 22. Midterm Mar. 27. Equality constraints: second-order conditions. Inequality constraints. (III.4,5) Mar. 29. Inequality constraints: KKT conditions, sufficient conditions (III.5,6) Apr. 3. Nonnegativity constraints, mixed constraints (III.8). Apr. 5. First-order differential equations. Separable equations, linear equations (V.1,3,4) Apr. 10. Second-order dif…