Lecture 7

Question 1

What is the multivariate Newtons (root-finding) method?

Answer 1

Question 2

What is the algorithm of Broydens method? Why is it used?

Answer 2

Question 3

What is a damped Newton method? What is its advantage?

Answer 3

Question 4

What are trust regions (for Newtons method)?

Answer 4

Question 5

What is the main idea behind optimization? What is an objective? What is an constraint?

Answer 5

Question 6

What is constrained optimization?

Answer 6

Question 7

What is the difference between local and global optimization?

Answer 7

Question 8

When does a minimum exist?

Answer 8

Question 9

What is coerciveness? What does it imply?

Answer 9

Question 10

Proof that coerciveness produces a minimum.

Answer 10

Question 11

When is a set convex? When is a function convex? (conceptually)

Answer 11

Question 12

When is a function convex (not the definition)?

Answer 12

Question 13

What is the definition of a critical point?

Answer 13

Question 14

What are the three types of critical points? (1d)

Answer 14

Question 15

When do you have each different type of critical point?

Answer 15

Question 16

What are eigenvalues and eigenvectors (definition)?

Answer 16

Question 17

What is diagonalization?

Answer 17

Question 18

How are symmetric matrices diagonalized?

Answer 18