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

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) 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 b...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 123; no. 2; pp. 409 - 429
Main Authors: Ruan, G. Z., Wang, S. Y., Yamamoto, Y., Zhu, S. S.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.11.2004
Springer Nature B.V
Subjects:
Applied sciences
Decision making
Exact sciences and technology
Game theory
Investigations
Linear programming
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Systems science
Variables
multilevel programming
Decision support system
Decision making
Optimality condition
Bilevel programming
Linear programming
Optimality criterion
connectedness
Objective function
upper semicontinuity
Semi continuous function
Semicontinuous
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) 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(/) 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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-004-5156-y