NDLI: Bilevel problems over polyhedra with extreme point optimal solutions

Content Provider	Springer Nature Link
Author	Galé, Carmen Lohse, Sebastian Dempe, Stephan Calvete, Herminia I.
Copyright Year	2011
Abstract	Bilevel programming involves two optimization problems where the constraint region of the upper level problem is implicitly determined by another optimization problem. In this paper we focus on bilevel problems over polyhedra with upper level constraints involving lower level variables. On the one hand, under the uniqueness of the optimal solution of the lower level problem, we prove that the fact that the objective functions of both levels are quasiconcave characterizes the property of the existence of an extreme point of the polyhedron defined by the whole set of constraints which is an optimal solution of the bilevel problem. An example is used to show that this property is in general violated if the optimal solution of the lower level problem is not unique. On the other hand, if the lower level objective function is not quasiconcave but convex quadratic, assuming the optimistic approach we prove that the optimal solution is attained at an extreme point of an ‘enlarged’ polyhedron.
Ending Page	586
Page Count	14
Starting Page	573
File Format	PDF
ISSN	09255001
e-ISSN	15732916
Journal	Journal of Global Optimization
Issue Number	3
Volume Number	53
Language	English
Publisher	Springer US
Publisher Date	2011-08-09
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Extreme point Operations Research/Decision Theory Computer Science Bilevel programming Quasiconcave Nonlinear programming Quadratic Optimization Real Functions
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

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