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Title: Optimal control problems governed by a variational inequality via nonlinear Lagrangian methods
Authors: Zhou, YY
Yang, XQ 
Teo, KL
Keywords: Nonlinear Lagrangian function
Optimal control
Variational inequality
Zero duality gap
Issue Date: 2006
Publisher: Taylor & Francis
Source: Optimization, 2006, v. 55, no. 1-2, p. 187-203 How to cite?
Journal: Optimization 
Abstract: In this article, by using nonlinear Lagrangian methods, we study an optimal control problem where the state of the system is defined by a variational inequality problem for monotone type mappings. We obtain one necessary condition and several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear Lagrangian dual problem. We show that every weak limit point of a sequence of optimal solutions generated by the power penalty problem is a solution for the optimal control problem. We apply our results to an example where the variational inequality leads to a linear elliptic obstacle problem.
ISSN: 0233-1934
EISSN: 1029-4945
DOI: 10.1080/02331930500530807
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