Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions - Ruan, G. Z.; Wang, S. Y.; Yamamoto, Y.; Zhu, S. S. (Journal of optimization theory and applications, 2004)
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.