Decision making under uncertainty: A semi-infinite programming approach
type: Item
instance of: scholarly article
title: Decision making under uncertainty: A semi-infinite programming approach
zbMATH Open document ID: 0554.90093
DOI: 10.1016/0377-2217(85)90314-5
author: Reinhard Weber
published in: European Journal of Operational Research
publication date: 1985-01-01T00:00:00Z
review text: Consider the semi-infinite linear vector optimization problem \[ (SIVP)\quad \max \sum^{N}_{k=1}c_ k(t)x_ k\quad for\quad all\quad t\in T\quad s.t.\quad \sum^{N}_{k=1}a_ k(s)x_ k\leq b(s)\quad for\quad all\quad s\in S, \] where T and S are two nonempty, arbitrary subsets of \({\mathbb{R}}^ m\), \(C_ 0(T)\) and \(C_ 0(S)\) are the vector spaces of all continuous functions on T, resp. S, \(c_ 1(t),...,c_ N(t)\in C_ 0(T)\) and \(a_ 1(s),...,a_ N(s)\), \(b(s)\in C_ 0(S)\). This problem specializes to a linear vector optimization problem if \(| T|\) and \(| S|\) are finite and to a semi-infinite programming problem in the case of \(| T| =1\). The author derives theoretical results for (SIVP) based on known basic results in vector optimization and semi-infinite programming theory. The (SIVP) is interpreted as a decision model under uncertainty where the objectives as well as the constraints themselves are affected by uncertain parameters and the author treats the case of an infinite number of occuring states of nature.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 3883965
zbMATH Keywords: semi-infinite linear vector optimization
zbMATH Keywords: decision model under uncertainty
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
full work available at URL: 0377-2217(85)90314-5
OpenAlex ID: W2082469626
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description: scientific article; zbMATH DE number 3883965