Continuous optimization, an introduction
نویسنده
چکیده
2 (First order) Descent methods, rates 2 2.1 Gradient descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 What can we achieve? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Second order methods: Newton’s method . . . . . . . . . . . . . . . . . 7 2.4 Multistep first order methods . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 Heavy ball method . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.2 Conjugate gradient . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.3 Accelerated algorithm: Nesterov 83 . . . . . . . . . . . . . . . . . 11 2.5 Nonsmooth problems? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.1 Subgradient descent . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.2 Implicit descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
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