Approximation analysis for the minimization problem of difference-of-convex functions with Moreau envelopes

2024/02/21 by Yan Tang, Tang, Yan, Shiqing Zhang +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2402.13461

openalex publication_date 2024/02/21 · openalex created_date 2024/02/23 · openalex updated_date 2026/07/28

Abstract

In this work the minimization problem for the difference of convex (DC) functions is studied by using Moreau envelopes and the descent method with Moreau gradient is employed to approximate the numerical solution. The main regularization idea in this work is inspired by Hiriart-Urruty [14], Moudafi[17], regularize the components of the DC problem by adapting the different parameters and strategic matrices flexibly to evaluate the whole DC problem. It is shown that the inertial gradient method as well as the classic gradient descent scheme tend towards an approximation stationary point of the original problem.

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