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

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  6. Lecture 6.1: optimizing more general functions, bu...

Lecture 6.1: optimizing more general functions, but univariate ones

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Towards more general optimization algorithms: since even restricted to a single variable optimization is impossible, impose conditions on the objective not to be "too adversarial". The "obvious" algorithm and its (easy) correctness proof. But global optimization still is "too hard" (even in one variable, not to mention many).

Lecture 6.1: optimizing more general functions, but univariate ones
◄ Lecture 5.2: sublinear convergence and where this leads us
Lecture 6.2: first steps with local optimization: the role of derivatives ►

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          • General Information

          • 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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