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Machine Learning: Introduction to Optimization Techniques
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Machine Learning: Introduction to Optimization Techniques
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13 Questions

1. When Newton's method is started from a point near the solution, it will converge very quickly.
2. $f(x) = -\log x$ is self-concordant.
3. If $f$ is self-concordant, its Hessian is Lipschitz continuous.
4. Newton's method with step size $h=1$ always works.
5. Newton's method would probably require fewer iterations than the gradient method, but each iteration would be much more costly.
6. Using Newton's method to minimize $f(Ty)$, where $Ty=x$ and $T$ is nonsingular, can greatly improve the convergence speed when $T$ is chosen appropriately.
7. $f(x) = -\log x$ is self-concordant.
8. $f(x) = \exp x$ is self-concordant.
9. Newton's method would probably require fewer iterations than the gradient method, but each iteration would be much more costly.
10. In descent methods, the particular choice of line search does not matter so much.
11. Newton's method with step size $h=1$ always works.
12. In descent methods, the particular choice of search direction does not matter so much.
13. Using Newton's method to minimize $f(Ty)$, where $Ty=x$ and $T$ is nonsingular, can greatly improve the convergence speed when $T$ is chosen appropriately.

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