Liu, W.B. and Gong, W. and Yan, N. (2009) A new finite element approximation of a state-constrained optimal control problem. Journal of Computational Mathematics, 27 (1). pp. 97-114. ISSN 0254-9409.
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In this paper, we study numerical methods for an optimal control problem with point-wise state constraints. The traditional approaches often need to deal with the delta-singularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms (nonconforming finite element approximation) are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Social Sciences > Kent Business School|
|Depositing User:||Steve Wenbin Liu|
|Date Deposited:||01 Mar 2010 11:41|
|Last Modified:||01 Mar 2010 11:41|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/22892 (The current URI for this page, for reference purposes)|
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