Time complexity of solvers


I am using sdpt3 to solve for l-1 minimization problem for basis pursuit algorithm(https://web.stanford.edu/group/SOL/papers/BasisPursuit-SIGEST.pdf). Are there any research articles that discuss about the worst-case time complexity of solvers? Here’s the code for the problem:

This is LP-representable, although i don’t know exactly how CVX formulates this for the solver.