Douglas Jr., J., and Gunn, J.E. (1964) A General Formulation of Alternating Direction Methods. Numerishe Mathematik, 6, 428-453. https://doi.org/10.1007/BF01386093

has been cited by the following article:

• TITLE: Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation

  AUTHORS: A. Lapin, E. Laitinen

  KEYWORDS: Parabolic Optimal Control, State Constraints, Finite Difference Method, Constrained Saddle Point Problem, Iterative Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.1, January 5, 2018

  ABSTRACT: We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.