A quick post to keep track of several things:

• Christian Leonard  has lecture notes on convex optimization with an application to optimal transport on his website.
• The paper Variational Properties of Value Functions by  Aravkin, Burke, and Friedlander discuss how the value of minimization problems like $\min \rho(Ax-b)\quad \mbox{s.t}\quad \phi(x)\leq tau$ depend on $\tau$ and $\latex b$. In inverse problems, the value function seems to contain important information on the the regularization process and hence, the results in this paper maybe helpful in designing and analyzing parameter choice rules.
• The paper Accelerated and Inexact Forward-Backward Algorithms by Villa,Salzo, Baldassarre, and Verri looks like an interesting development in the fiel of splitting methods.
• The paper  Consistency of the posterior distribution in generalized linear inverse problems by Natalia Bochkina is another contribution on “probabilitic inverse problems” where one does not only try to infer a regularized solution to an ill posed problems but also how the uncertainty in the data in propagated through the regularization process.