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    • 18. 发明授权
    • Method of efficient gradient computation
    • 高效梯度计算方法
    • US5886908A
    • 1999-03-23
    • US825278
    • 1997-03-27
    • Andrew Roger ConnRudolf Adriaan HaringChandramouli Visweswariah
    • Andrew Roger ConnRudolf Adriaan HaringChandramouli Visweswariah
    • G06F17/50G06F9/455
    • G06F17/5036G06F17/5063
    • A method of efficient computation of gradients of a merit function of a system includes the steps of: specifying at least one parameter for which the gradients with respect to the at least one parameter are desired; specifying the merit function of interest in terms of observable measurements of the system; either solving or simulating the system to determine values of the measurements; expressing the gradients of the merit function as the gradient of a weighted sum of measurements; forming an appropriately configured adjoint system; and either solving or simulating the adjoint system to simultaneously determine the gradients of the merit function with respect to the at least one parameter by employing a single adjoint analysis. Preferably, the system may be modeled by a set of equations comprising at least one of the following: a nonlinear set of equations, a linear set of equations, a set of linear partial differential equations, a set of nonlinear partial differential equations, a set of linear differential algebraic equations or a set of nonlinear differential algebraic equations. Further, the system of interest may be a network and, preferably, may be an electrical circuit. Still further, elements of the adjoint network and excitations of the adjoint network are determined in order to obtain the gradients of the merit function by employing a single adjoint analysis. It is to be appreciated that, in a preferred embodiment, the gradients of merit function are computed for the purpose of optimization and the merit function may be either a Lagrangian merit function or an augmented Lagrangian merit function.
    • 一种有效计算系统的优值函数的梯度的方法包括以下步骤:指定至少一个参数,该参数相对于至少一个参数的梯度是期望的; 根据系统的可观测量指定感兴趣的优点功能; 解决或模拟系统以确定测量值; 将优值函数的梯度表示为加权求和和的梯度; 形成适当配置的伴随系统; 并且通过采用单一伴随分析来解决或模拟伴随系统以同时确定关于至少一个参数的优值函数的梯度。 优选地,可以通过包括以下至少一个的一组方程来建模系统:非线性方程组,线性方程组,一组线性偏微分方程,一组非线性偏微分方程,一组 的线性微分代数方程或一组非线性微分代数方程。 此外,感兴趣的系统可以是网络,并且优选地可以是电路。 此外,确定伴随网络的元素和伴随网络的激励,以便通过采用单个伴随分析来获得优值函数的梯度。 应当理解,在优选实施例中,为优化目的而计算优值函数的梯度,并且优值函数可以是拉格朗日优值函数或增强的拉格朗日优值函数。