I know Boyd's famous Convex Optimization, but for me it's a little bit old because it was written in 2003 and some progresses have been made during this decade. The book Optimization for Machine Learning fill the gap nicely but it's not a textbook: the chapters are independent, and it doesn't have exercises. So any recommendations for textbooks on modern optimization? Thanks.
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"Convex Optimization" is a good book. The first part covers mathematical formulations of optimization methods and concentrates on theoretical aspects of methods. The second part mentions in details algorithmic aspects.
You can also refer to "Nonlinear Programming" by Dimitri P. Bertsekas and it has assignments too. This is a great book for anyone who wants to deepen into the details.