Resources on Solving Convex Optimization Problems in the Compress Sensing Field

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?

Answer

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.