Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems

Abstract

Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.

Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.

Cite this paper

E. Laitinen and A. Lapin, "Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1862-1867. doi: 10.4236/am.2012.312253.

E. Laitinen and A. Lapin, "Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems,"

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