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Luca Kollmer
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Decks in this class (19)
1. Intro to Optimisation
Definition optimisation problem 1,
Definition feasible set 2,
Definition local minimiser 3
4
cards
2. Prerequisites
Definition symmetric matrix 1,
Definition condition number 2,
Definition self adjoint 3
8
cards
3. Convexity I
Definition 31 convex set convex b...,
Lemma 32 three properties of conv...,
Definition convex hull convex com...
7
cards
4. Convexity II
Definition 41 convex function str...,
Theorem 42 local minimisers of co...,
Theorem 46 1 f in c 1 rr n convex...
3
cards
6. Iterative Algorithms II
Definition descent direction opti...,
Definition sufficient decrease co...,
Definition 62 convergence 3
5
cards
7. Newton's Method
Definition newton s method 1,
Lemma 71 descent direction of new...,
Do not compute inverse of hessian...
5
cards
8. Linear Programming I: Polyhedra
Definition linear program 1,
Definition 82 polyhedron supporti...,
Definition 86 polytope 3
5
cards
9. Linear Programming II: Duality
Definition convex cone 1,
Lemma 91 hyperplane separation fo...,
Theorem 92 farkas lemma 3
7
cards
10. Lagrange Duality
Definition convex problem 1,
Theorem 101 in convex f x is mini...,
Lagrange duality lagrangian 3
6
cards
11. KKT Optimality Conditions
Theorem 111 slate s conditions 1,
Definition duality gap 2,
Theorem 114 kkt conditions 3
4
cards
13. Introduction to Approximation Theory
Definition space of trigonometric...,
Lemma 132 comparison of 2 and max...
2
cards
14. Polynomial Approximation in the max-norm I
Definition space of polynomials o...,
Theorem 141 weierstrass approxima...,
Minimax polynomial problem 3
4
cards
15. Polynomial Approximation in the max-norm II
Theorem 151 oscillation theorem 1,
Definition 153 chebyshev polynomi...,
Lemma 154 the chebyshev polynomia...
5
cards
16. Polynomial Approximation in the 2-norm I
Definition lebesque space best ap...,
Definition 162 system of orthogon...
2
cards
17. Polynomial Approximation in the 2-norm II
Theorem 172 existence of minimax ...,
Bessel inequality 2,
Theorem 173 p_n is best 2 norm ap...
3
cards
18. Approximation by Rational Functions
Pade approximation 1
1
cards
19. Trigonometric Approximation and Fourier Series
Definition space of all trigonome...,
Space of 2 pi periodic trigonomet...,
Linearly independent and orthogon...
7
cards
20. Fourier Series II
Definition error pointwise conver...,
Definition uniform error uniform ...,
Discrete fourier transform 3
4
cards
23. Best-fit Subspaces and SVD II
Theorem 231 best fit n dimensiona...,
Lemma 232 if a has positive and r...,
Definition matrix 2 norm spectral...
6
cards
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MA265 MMM3
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