On the convexification procedure for nonconvex and nonsmooth infinite dimensional optimization problems
type: Item
instance of: scholarly article
title: On the convexification procedure for nonconvex and nonsmooth infinite dimensional optimization problems
zbMATH Open document ID: 0755.49013
DOI: 10.1016/0022-247X(91)90359-8
author: Helmut Dietrich
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The paper gives a generalization and modification of a convexification procedure of \textit{D. P. Bertsekas} [J. Optimization Theory Appl. 29, 169- 197 (1979; Zbl 0389.90080)] for infinite dimensional, nonsmooth and nonconvex optimization problems. A nonconvex minimization problem is being transformed into a convex parametrical minimization problem and an additional minimization of an everywhere Fréchet differentiable nonconvex function. The convexification of the nonconvex cost function \(f\) to ensue by means of a strongly convex function \(g\), so that \(f+g\) is also a strongly convex function. One can prove a connection with the duality theory of \textit{J. F. Toland} [J. Math. Anal. Appl. 66, 399-415 (1978; Zbl 0403.90066)] and give a descent method for the original problem.
reviewed by: Hans-Dietrich Hecker
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 57290
zbMATH Keywords: convexification
zbMATH Keywords: infinite dimensional, nonsmooth and nonconvex optimization
zbMATH Keywords: descent method
MaRDI profile type: Publication
cites work: Convexification procedures and decomposition methods for nonconvex optimization problems
cites work: Globally convergent decomposition methods for nonconvex optimization problems
cites work: Submonotone mappings and the proximal point algorithm
cites work: Duality in nonconvex optimization
cites work: On uniformly convex functions
description: scientific article; zbMATH DE number 57290