2011, 2011(Special): 1101-1110. doi: 10.3934/proc.2011.2011.1101

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, Japan

2. 

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

3. 

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

Received  August 2010 Revised  April 2011 Published  October 2011

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.
Citation: Yusuke Murase, Atsushi Kadoya, Nobuyuki Kenmochi. Optimal control problems for quasi-variational inequalities and its numerical approximation. Conference Publications, 2011, 2011 (Special) : 1101-1110. doi: 10.3934/proc.2011.2011.1101
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