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Applied Mathematical Methods by Bhaskar Dasgupta

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Chapter 24

1 Both terms are open to attack by a purist, for different reasons; but the interpretation is correctly understood.

2 Gradients of other vector quantities, appearing later in this chapter, follow the same protocol.

3 Exercise 6 of Chap. 4 gives an example of an efficient processing of such active set updates.

4 Mostly, we expect μi(a) > 0. But, in degenerate cases, μi(a) = 0 along with gi(a) (x*) is also possible. How do you interpret such a case?

5 See exercise 3, Chap. 6

6 See exercise 9 of Chap. 4, for the projection formula.

7 also called the method of multipliers

8 Exercise 5 of Chap. 8 exhibits the smoothening of the eigenstructure of Hϕ(λ) by the penalty term.

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