Sensitivity analysis for variational inequalities defined on polyhedral sets

Sensitivity analysis for variational inequalities defined on polyhedral sets

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Article ID: iaor1989751
Country: United States
Volume: 14
Issue: 3
Start Page Number: 410
End Page Number: 432
Publication Date: Aug 1989
Journal: Mathematics of Operations Research
Authors: ,
Keywords: calculus of variations
Abstract:

Variational inequalities have often been used as a mathematical programming tool in modeling various equilibria in economics and transportation science. The behavior of such equilibrium solutions as a result of the changes in problem data is always of concern. In this paper, the authors present an approach for conducting sensitivity analysis of variational inequalities defined on polyhedral sets. They introduce the notion of differentiability of a point-to-set mapping and derive continuity and differentiability properties regarding the perturbed equilibrium solutions, even when the solution is not unique. As illustrated by several examples, the assumptions made in this paper are in a certain sense the weakest possible conditions under which the stated properties are valid. The authors also discuss applications to some equilibrium problems such as the traffic problem.

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