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Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

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Pubblicato in:Journal of Optimization Theory and Applications vol. 123, no. 2 (Nov 2004), p. 409
Autore principale: Ruan, G Z
Altri autori: Wang, S Y, Yamamoto, Y, Zhu, S S
Pubblicazione:
Springer Nature B.V.
Soggetti:
Game theory
Variables
Linear programming
Mathematics
Investigations
Systems science
Decision making
Accesso online:Citation/Abstract
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Abstract:In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-004-5156-y
Fonte:ABI/INFORM Global