Moreau-Rockafellar type theorem for convex set functions
type: Item
instance of: scholarly article
title: Moreau-Rockafellar type theorem for convex set functions
zbMATH Open document ID: 0656.90097
DOI: 10.1016/0022-247X(88)90084-4
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let (X,\(\Gamma\),\(\mu)\) be a finite atomless measure space and \(F_ 1,F_ 2,...,F_ n\), \(G_ 1,G_ 2,...,G_ m\) be convex real-valued set functions defined on a convex subfamily \({\mathcal S}\) of the \(\sigma\)- field \(\Gamma\). Consider an optimization problem as follows: (P) Minimize \(F(\Omega)=(F_ 1(\Omega),F_ 2(\Omega),...,F_ n(\Omega))\) subject to \(\Omega\in {\mathcal S}\) and \(G_ j(\Omega)\leq 0\) \((j=1,2,...,m)\). The authors prove a theorem of Moreau-Rockafellar type for set functions, and then use the theorem to prove a Kuhn-Tucker type condition for an optimal solution of the minimization problem (P) for real valued set functions. If the set functions are vector-valued, the Fritz John type condition for an optimum of the multiobjective minimization problem (P) is established.
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 4072741
zbMATH Keywords: Moreau-Rockafellar theorem
zbMATH Keywords: finite atomless measure space
zbMATH Keywords: convex real- valued set functions
zbMATH Keywords: Kuhn-Tucker type condition
zbMATH Keywords: Fritz John type condition
author: Hang-Chin Lai
author: Lai-Jiu Lin
reviewed by: Z. J. Liu
MaRDI profile type: Publication
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full work available at URL: 0022-247x(88)90084-4
OpenAlex ID: W1979955085
description: scientific article; zbMATH DE number 4072741