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Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide. (English) Zbl 1477.65099

Summary: This work deals with the numerical solution of a bilateral obstacle optimal control problem which is similar to the one given in [M. Bergounioux and S. Lenhart, SIAM J. Control Optim. 43, No. 1, 240–255 (2004; Zbl 1079.49023)] with some modifications. It can be regarded as an extension of our previous work [J. Appl. Math. Comput. 45, No. 1–2, 375–409 (2014; Zbl 1293.49066)], where the main feature of the present work is that the controls and the two obstacles are the same. For the numerical resolution we follow the idea of our previous work [loc. cit.]. We begin by discretizing the optimality system of the underlying problem by using finite differences schemes, then we propose an iterative algorithm. Finally, numerical examples are provides to show the efficiency of the proposed algorithm and the used scheme.

MSC:

65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
49M05 Numerical methods based on necessary conditions
49M25 Discrete approximations in optimal control
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