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Machine Learning by Sergios Theodoridis

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6.11 The Coordinate and Cyclic Coordinate Descent Methods

So far, we have discussed the steepest descent and Newton’s method for optimization. We will conclude the discussion with a third method, which can also be seen as a member of the steepest descent family of methods. Instead of the Euclidean and quadratic norms, let us consider the following minimization task for obtaining the normalized descent direction,

v=argminzzTJ,

si183_e  (6.57)

s.t.||z||1=1,

si184_e  (6.58)

where ||⋅||1 denotes the 1 norm, defined as

||z||1:=i=1l|zi|.

Most of Chapter 9 ...

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