A New Finite Element Approximation of a State-Constrained Optimal Control Problem

A New Finite Element Approximation of a State-Constrained Optimal Control Problem

Year:    2009

Author:    Wenbin Liu, Wei Gong, Ningning Yan

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 1 : pp. 97–114

Abstract

In this paper, we study numerical methods for an optimal control problem with pointwise 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-JCM-8562

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 1 : pp. 97–114

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Optimal control problem State-constraints Fourth order variational inequalities Nonconforming finite element method.

Author Details

Wenbin Liu

Wei Gong

Ningning Yan