On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems
نویسندگان
چکیده
Iterative methods for nite-dimensional inclusions which arise in applying a nite-element or a nite-di erence method to approximate state-constrained optimal control problems have been investigated. Speci cally, problems of control on the righthand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the nding of the control function or Lagrange multipliers are proved. 2000 Mathematics Subject Classi cation: 65K15, 65N30, 49M29, 49M30.
منابع مشابه
Dynamical Control of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear Equations
One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...
متن کاملOn Parametric Evolution Inclusions of the Subdifferential Type with Applications to Optimal Control Problems
In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusio...
متن کاملA Computational Method for Solving Optimal Control Problems and Their Applications
In order to obtain a solution to an optimal control problem, a numerical technique based on state-control parameterization method is presented. This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time. Several numerical examples are presented to confirm the analytical findings and illus...
متن کاملAn iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...
متن کاملA Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method
In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Comput. Meth. in Appl. Math.
دوره 10 شماره
صفحات -
تاریخ انتشار 2010