How to regularize a difference of convex functions
type: Item
instance of: scholarly article
title: How to regularize a difference of convex functions
zbMATH Open document ID: 0807.46041
DOI: 10.1016/0022-247X(91)90187-5
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: Given a nonconvex function \(f\) defined as the difference of two convex functions \(g\) and \(h\) (\(f\) is a so-called d.c. function), the author studies the regularized (or smoothed) version \(f_ r= g\square r/2\| \cdot\|^ 2- h\square r/2\| \cdot\|^ 2\) of \(f\) obtained by performing the infimal convolution of both component functions \(g\) and \(h\) by the same kernel function \(r/2\|\cdot \|^ 2\). He compares critical points of \(f_ r\) and \(f\) and considers the behavior of critical points of \(f_ r\) as \(r\to +\infty\). To a great extent the nice properties of the regularization process \(\varphi\to\varphi \square r/2\| \cdot\|^ 2\) when applied to convex functions \(\varphi\) are preserved for the process \(f\to f_ r\) when performed on d.c. functions \(f\).
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 61589
zbMATH Keywords: difference of two convex functions
zbMATH Keywords: convolution
zbMATH Keywords: kernel function
zbMATH Keywords: critical points
zbMATH Keywords: regularization process
author: Jean-Baptiste Hiriart-Urruty
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 61589