A proximal gradient method for control problems with nonsmooth and\n nonconvex control cost

2020/07/22 by Carolin Natemeyer, Natemeyer, Carolin, Daniel Wachsmuth +1 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2007.11426

openalex publication_date 2020/07/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We investigate the convergence of an application of a proximal gradient\nmethod to control problems with nonsmooth and nonconvex control cost. Here, we\nfocus on control cost functionals that promote sparsity, which includes\nfunctionals of L^p-type for p\∈ [0,1). We prove stationarity properties of\nweak limit points of the method. These properties are weaker than those\nprovided by Pontryagin's maximum principle and weaker than L-stationarity.\n

Cited by

• A smoothed proximal trust-region algorithm for nonconvex optimization problems with L^p-regularization, p∈ (0,1)

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