Some recommended exercises from the book 
"Convex Optimization" by Boyd and Vandenberghe

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 Convex sets:
   2.8, 2.12, 2.16, 2.23
 
 Convex functions:
   3.1, 3.15, 3.17, 3.22
 
 Duality:
   5.12, 5.14, 5.21, 5.22
 
 Barrier method:
   11.2, 11.3
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