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Luca Kollmer
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Decks in this class (20)
1. Intro to Optimisation
Definitionoptimisation problem,
Definitionfeasible set,
Definitionlocal minimiser
4
cards
2. Prerequisites
Definitionsymmetric matrix,
Definitioncondition number,
Definitionself adjoint
8
cards
3. Convexity I
Definition 31convex setconvex body,
Lemma 32three properties of conve...,
Definitionconvex hullconvex combi...
7
cards
4. Convexity II
Definition 41convex functionstric...,
Theorem 42local minimisers of con...,
Theorem 461 f in c 1 rr n convex ...
3
cards
5. Iterative Algorithms I
Definitioniterative algorithmstep...,
Gradient descent,
Cauchy schwarz gives bounds
4
cards
6. Iterative Algorithms II
Definitiondescent directionoptima...,
Definition sufficient decrease co...,
Definition 62convergence
5
cards
7. Newton's Method
Definitionnewton s method,
Lemma 71descent direction,
Do not compute inverse of hessian...
5
cards
8. Linear Programming I: Polyhedra
Definitionlinear program,
Definition 82polyhedronsupporting...,
Definition 86polytope
5
cards
9. Linear Programming II: Duality
Definitionconvex cone,
Lemma 91 hyperplane separation fo...,
Theorem 92 farkas lemma
7
cards
10. Lagrange Duality
Definitionconvex problem,
Theorem 101in convex f x is minim...,
Lagrange dualitylagrangian
6
cards
11. KKT Optimality Conditions
Theorem 111 slate s conditions,
Definition,
Theorem 114 kkt conditions
4
cards
13. Introduction to Approximation Theory
Definitionspace of trigonometric ...,
Lemma 132comparison of 2 and max ...
2
cards
14. Polynomial Approximation in the max-norm I
Definitionspace of polynomials of...,
Theorem 141 weierstrass approxima...,
Minimax polynomial problem
4
cards
15. Polynomial Approximation in the max-norm II
Theorem 151 oscillation theorem,
Definition 153chebyshev polynomia...,
Lemma 154the chebyshev polynomial...
5
cards
16. Polynomial Approximation in the 2-norm I
Definitionlebesque spacebest appr...,
Definition 162system of orthogona...
2
cards
17. Polynomial Approximation in the 2-norm II
Theorem 172existence of minimax p...,
Bessel inequality,
Theorem 173p_n is best 2 norm app...
3
cards
18. Approximation by Rational Functions
Definitionrational function,
Pade approximation
2
cards
19. Trigonometric Approximation and Fourier Series
Definitionspace of all trigonomet...,
Space of 2pi periodic trigonometr...,
Linearly independent and orthogon...
7
cards
20. Fourier Series II
Definitionerror and pointwise con...,
Definitionuniform erroruniform co...,
Discrete fourier transform
4
cards
23. Best-fit Subspaces and SVD II
Theorem 231best fit n dimensional...,
Lemma 232if a has positive entrie...,
Definitionmatrix 2 norm spectral ...
6
cards
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