The Lagrangian relaxation strategy (or dualization) is one of the most important methodologies of optimization for solving structured large-scale mathematical programming problems. The line search procedure is very often encountered in solving the dual problem by using some ascent algorithm, such as a bundle algorithm, or an interior point algorithm, etc.. The existing line search methods, for ...

We provide a new perspective to understand proximal gradient algorithms. We show that both proximal gradient algorithm (PGA) and Bregman proximal gradient algorithm (BPGA) can be viewed as generalized proximal point algorithm (GPPA), based on which more accurate convergence rates of PGA and BPGA are obtained directly. Furthermore, based on GPPA framework, we incorporate the back-tracking line s...