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

2025/08/21 by Harbir Antil, Antil, Harbir, Anna Lentz +1
Computer Science · Engineering · #49M15 #49M37 #65K05 #65K10 #90C26 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2508.15446

openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate a trust-region algorithm to solve a nonconvex optimization problem with L^p-regularization for p∈(0,1). The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently by a line search along a suitable proximal path. To handle the nonconvexity and nonsmoothness of the L^p-pseudonorm, we replace it by a smooth approximation and construct a convex upper bound of that approximation. This enables us to use results of a trust-region method for composite problems with a convex nonsmooth term. We prove convergence properties of the resulting smoothed proximal trust-region algorithm and investigate its performance in some numerical examples. Furthermore, approximate subproblem solvers for the arising trust-region subproblems are considered.

Citations

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