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Computational Mathematics for Learning and Data Analysis - AA 2024/25

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  6. Lecture 5.1: convergence rates: from the gradient ...

Lecture 5.1: convergence rates: from the gradient method to the world

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Our first convergence and efficiency proofs, what it reliably tells and what it does not (only a bound on the convergence speed, so the practice may be different). Plotting convergence rates in practice: the theory nails it quite well, but not perfectly (it's a bound, after all), in the positive definite case. Naming names: convergence rates (linear, sublinear, superlinear), what they mean, what they look like on the log-linear plot.

Lecture 5.1: convergence rates: from the gradient method to the world
◄ Lecture 4.2: the gradient method for quadratic functions, practice
Lecture 5.2: sublinear convergence and where this leads us ►

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          • Slides: Numerical Linear Algebra

          • Slides: Optimization

          • Optimization & Learning Lecture Notes

          • Lecture Recordings: Numerical Linear Algebra

          • Lectures Recordings: Optimization

            • FileLecture 1.1 - introduction to the course

            • FileLecture 1.2 - motivation for the course: four exam...

            • FileLecture 2.1: general notions of optimization

            • FileLecture 2.2: starting very very easy and very slow...

            • FileLecture 3.1: multivariate optimization: initial co...

            • FileLecture 3.2: "real" quadratic functions and how th...

            • FileLecture 4.1: quadratic optimization: from optimali...

            • FileLecture 4.2: the gradient method for quadratic fun...

            • FileLecture 5.1: convergence rates: from the gradient ...

            • FileLecture 5.2: sublinear convergence and where this ...

            • FileLecture 6.1: optimizing more general functions, bu...

            • FileLecture 6.2: first steps with local optimization: ...

            • FileLecture 7.1: dichotomic search, from naive to mod...

            • FileLecture 7.2: faster local optimization and the rol...

            • FileLecture 8.1: closing thoughts of univariate optimi...

            • FileLecture 8.2: theory of gradients and Hessians towa...

            • FileLecture 9.1: local first- and second-order optimal...

            • FileLecture 10.1: the gradient method with "exact" lin...

            • FileLecture 10.2: inexact line search, the Armijo-Wolf...

            • FileLecture 11.1: convergence with the A-W LS, theory

            • FileLecture 11.2: the A-W LS in practice

            • FileLecture 12.1: "extremely inexact LS": fixed stepsize

            • FileLecture 12.2: gradient twisting approaches at thei...

            • FileLecture 13.1: all around Newton's method

            • FileLecture 13.2: towards the very-large-scale, quasi-...

            • FileLecture 14.1: deflected gradient methods I - Conju...

            • FileLecture 14.2: deflected gradient methods II - Heav...

            • FileLecture 15.1: the scary world of nondifferentiable...

            • FileLecture 15.2: (convex) nondifferentiable optimizat...

            • FileLecture 16.1: better nondifferentiable approachess...

            • FileLecture 16.2: first steps on constrained optimization

            • FileLecture 17.1: algebraic representation of feasibl...

            • FileLecture 17.2: from the KKT conditions to duality

            • FileLecture 18.1: first step in constrained optimization

            • FileLecture 18.2: more (projected gradient) steps in c...

            • FileLecture 19.1: from Frank-Wolfe to the dual method

            • FileLecture 19.2: ending with a bang: the (primal-dual...

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