Conjugate Gradient-Boundary Element Method to Distributed Optimal Control Problem
分布参数最优控制的边界元共轭梯度算法

The numerical solution of distributed optimal control of a linear elliptic problem is investigated. The system of optimality consisting of state and costate variables (Lagrangian multiplier)for the optimal control is derived, and in convex condition, uniqueness of optimal solution is proved. The optimal control problem is translated into a kind of two players game problem which is a non-cooperative Stackelberg game between control function and state function. The Nash equilibrium point for the new system is the solution of the optimal control problem. The conjugate gradient-boundary element method for solving the Nash equilibrium point is developed. Finally, theerror estimates for these schemes are obtained. Numerical resultsindicate that the approach can save substantial computational work and that the algorithm is effective.