A novel line search method for nonsmooth optimization problems

Abstract

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 differentiable 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.

Parallel low-complexity M-PSK detector for large-scale MIMO systems

“…To achieve this goal, we exploit the fact that the objective function in (5a) of problem (5) is convex in each variable x n , ∀n ∈ N . Employing the Jacobi algorithm [25][26][27], we can formulate the approximate function of the original objective function f (x) = ||y − Hx|| 2 , whose convergence to the optimal solution of the original problem is ensured with an appropriate step-size selection. Let x t denote the approximate solution to the problem (5) obtained in the (t − 1)th iteration.…”

“…The vectorx t − x t represents a descent direction of the objective function f (x) in the domain of problem (5) [26]. Therefore, the vector x t is updated after each iteration, using the following rule:…”

“…(8), which minimizes the objective function f (x) in the domain of problem (5), can be computed using the exact line search method [26,30] as…”