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2011, Volume 2011: 1101-1110. Doi: 10.3934/proc.2011.2011.1101 open access
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Optimal control problems for quasi-variational inequalities and its numerical approximation

  • 1.

    Department of Mathematics, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya, 468-8502

  • 2.

    Faculty of Economic Sciences, Hiroshima Shudo University, 1-1-1 Ozukahigashi, Asaminami-ku, Hiroshima, 731-3195

  • 3.

    Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301

Received:  July 31, 2010
Revised:  March 31, 2011
Published:  August 2017
Abstract Related Papers Cited by
    Abstract
  • The main objective of this paper is to discuss about optimal control problems in which the state equations may have multiple solutions. Our state equations are represented by the so-called quasi-variational inequalities and some difficulties for the mathematical treatment arise from such a structure. From the numerical point of view we propose a class of regular approximations for them in which state equations are uniquely solved and the control spaces are relaxed, and further a class of their time-discretizations which are schemes of usual elliptic optimal control problems.
    Mathematics Subject Classification: Primary: 35K45; Secondary: 35K50.

    Citation:
    shu

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