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When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge after few iterations and solve the problem.

But, when I try to add some other constraints to the cost function, I cannot derive the iterative or whatever the solution is and I know that is for my poor mathematics.

Can anyone lead me to a book or so to read and understand how to solve these types of mathematics? What book chapter? What tutorial?

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There are few options:

  1. Stephen Boyd, Lieven Vandenberghe - Convex Optimization.
    This is the classic in this field. Very well written book.
    Also have a look on other papers of Boyd on similar subjects such as the The Alternating Direction Method of Multipliers (ADMM).
    They also have a great MOOC Course Stanford Online CVX 101 - Convex Optimization.

  2. Amir Beck - Introduction to Nonlinear Optimization - Theory, Algorithms and Applications & Amir Beck - First-Order Methods in Optimization.
    Amir is a great teacher and his book are both deep, practical and easy to read.

  3. CMU Statistics 36-725 - Convex Optimization: Fall 2016 by Ryan Tibshirani.
    Videos are available on YouTube.

I think once you skim through those you'll be able to handle most of the cases in Convex Optimization.

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