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A.P.Sage.N.J.Smith和E.J.Bauman等学者认为不能用迭代的方法,如梯度法求得奇异控制问题的最优解。本文提出了一种新的梯度——诱导梯度。利用诱导梯度就能够用迭代的方法求得奇异控制问题的最优解。本文从理论上证明了这种算法的收敛性,并对一个数学模型进行了计算,得到了满意的结果。共轭梯度法适用于求解函数Z=ax~2+by~2的极值点问题,而本文提出的诱导梯度法适用于求解函数Z=axy+bx+cy+d的鞍点问题。
A.P. Sage.N.J. Smith and E.J. Bauman and other scholars believe that can not be iterative methods, such as the gradient method for solving the singular control problem optimal solution. In this paper, a new gradient-induced gradient is proposed. The use of induction gradient can be iterative method for solving the singular control problem optimal solution. In this paper, the convergence of this algorithm is theoretically proved, and a mathematical model is calculated, and the satisfactory result is obtained. The conjugate gradient method is suitable for solving the extreme point problem of the function Z = ax ~ 2 + by ~ 2. However, the induced gradient method proposed in this paper is suitable for solving the saddle point problem of the function Z = axy + bx + cy + d.