# Confusion related to solving the optimization in linear svm using dual coordinate descent

I have this confusion related to L1 and L2 svm. I was reading this paper

I am attaching the screenshot and the part I didn't understand

The part that I didn't understand how it was derived

I didn't understand how we got the $D_{ii}$ matrix and what is this about U

Also I didn't understand some derivation related to the dual coordinate descent method as given in the paper

I didn't understand what this projected gradient means and how the highlighted equations were derived.

I think this is a pretty popular paper but I am not getting how it is solved. Any suggestions will be much appreciated.

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