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

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  6. Lecture 10.1: the gradient method with "exact" lin...

Lecture 10.1: the gradient method with "exact" line search

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Multivariate unconstrained optimization. Choice of the direction: the obvious one = steepest descent. Choice of the stepsize, the obvious one: "exact" stepsize. Convergence analysis for approximate line search to an approximate stationary point. Stopping conditions, what you would like to have, what you can have, the relationships between the two. "Real" inexact line search: Armijo-Wolfe conditions, what they mean, why they work.

Lecture 10.1: the gradient method with "exact" line search
◄ Lecture 9.1: local first- and second-order optimality conditions (necessary and sufficient), convexity in \R^n
Lecture 10.2: inexact line search, the Armijo-Wolfe conditions ►

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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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