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A. Lapin and M. Khasanov, “State-Constrained Optimal Control of an Elliptic Equation with Its Right-Hand Side Used as Control Function,” Lobachevskii Journal of Mathematics, Vol. 32, No. 4, 2011, pp. 453-462. doi:10.1134/S1995080211040287

has been cited by the following article:

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

  AUTHORS: Erkki Laitinen, Alexander Lapin

  KEYWORDS: Constrained Optimal Control Problem; Saddle Point Problem; Finite Element Method; Iterative Algorithm

  JOURNAL NAME: Applied Mathematics, Vol.3 No.12, December 12, 2012

  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.