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Optimality conditions for elliptic variational inequalities

  • Control of Distributed Parameter Systems
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  • First Online:
Analysis and Optimization of Systes

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 144))

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Abstract

By the penalty method, Ekeland’s Variational Principle and lower-semicontinuity of some set-valued mappings, necessary conditions of optimal control for some abstract elliptic variational inequalities are obtained in the cases where the convex sets satisfy some smoothness conditions. The idea is to find optimality conditions first for some penalized problems by Ekeland’s Variational Principle then to pass limits to obtain the optimality conditions. It is shown that these conditions lead to some known optimality conditions in many cases. They also yield new necessary conditions for some problems. Our results give uniform forms for several known optimality conditions for elliptic variational inequalities.

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    Liu Wenbin & J. E. Rubio

Authors
  1. Liu Wenbin
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  2. J. E. Rubio
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Editor information

A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Wenbin, L., Rubio, J.E. (1990). Optimality conditions for elliptic variational inequalities. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120038

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  • DOI: https://doi.org/10.1007/BFb0120038

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52630-8

  • Online ISBN: 978-3-540-47085-4

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