On some optimization problems under uncertainty
type: Item
instance of: scholarly article
title: On some optimization problems under uncertainty
zbMATH Open document ID: 0629.90066
DOI: 10.1016/0165-0114(86)90005-9
author: Florica Luban
author: Vincentiu Dumitru
published in: Fuzzy Sets and Systems
publication date: 1986-01-01T00:00:00Z
review text: The first part of the paper is devoted to the problem of inexact mathematical programming: Maximize \(f(c,x)\), subject to \(g_ i(a_ i,x)\leq 0\) \((i=1,\dots,m)\), where \(x\in R^ n\), \(c,a_ i\) are unknown parameters being supposed to lie in prescribed sets \(C\), \(A_ i\), respectively. Several strategies for solving such problems, e.g. Wald's criterion, Savage-Niehans, Hurwitz and Laplace criteria are discussed for the convex case of \(f,g_ i\), \(C\) and \(A_ i.\) The results obtained are applied to nonlinear multiobjective optimization problems and an application to capital budgeting of interrelated projects under uncertainty is also presented. The last part deals with nonlinear fuzzy mathematical programming. An extended Bellman-Zadeh's approach to the optimal decision in a fuzzy environment is presented.
reviewed by: Jaroslav Ramík
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C90
zbMATH DE Number: 4025165
zbMATH Keywords: inexact mathematical programming
zbMATH Keywords: nonlinear multiobjective optimization
zbMATH Keywords: capital budgeting
zbMATH Keywords: nonlinear fuzzy mathematical programming
MaRDI profile type: Publication
full work available at URL: 0165-0114(86)90005-9
OpenAlex ID: W2050491270
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description: scientific article; zbMATH DE number 4025165