A novel line search method for nonsmooth optimization problems

In this paper, we propose a novel exact/successive line search method for stepsize calculation in iterative algorithms for nonsmooth optimization problems. The proposed approach is to perform line search over a properly constructed differ-entiable function based on the original nonsmooth objective function, and it outperforms state-of-the-art techniques from the perspective of convergence speed, computational complexity and signaling burden. When applied to LASSO, the proposed exact line search is shown, either analytically or numerically, to exhibit several desirable advantages, namely: it is implementable in closed-form, converges fast and is robust with respect to the choice of problem parameters.