2020/09/03 by Merino, Pedro, Reyes, Juan Carlos De Los
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2009.01878
In this paper we propose a second--order method for solving linear composite sparse optimization problems consisting of minimizing the sum of a differentiable (possibly nonconvex function) and a nondifferentiable convex term. The composite nondifferentiable convex penalizer is given by ℓ1--norm of a matrix multiplied with the coefficient vector. The algorithm that we propose for the case of the linear composite ℓ1 problem relies on the three main ingredients that power the OESOM algorithm \citedlrlm07: the minimum norm subgradient, a projection step and, in particular, the second--order information associated to the nondifferentiable term. By extending these devices, we obtain a full second--order method for solving composite sparse optimization problems which includes a wide range of applications. For instance, problems involving the minimization of a general class differential graph operators can be solved with the proposed algorithm. We present several computational experiments to show the efficiency of our approach for different application examples.