摘要
本文通过Hamiltonian函数和Taylor定理,导出了一般优化参数选择问题的评价函数的梯度公式.在例题中,利用Lagrange乘子和该梯度公式,对于在自重和均布荷载作用下缆索的最轻重量设计,获得了一组优化的必要条件.所提供的方法表明,在求解这类优化问题,其中包括端点上带有代数约束的微分方程组问题是简单有效的.
In this paper, the gradient expression of the cost functional for the (?)roblem of the general optimal parameter selection is derived by means of the Hamiltonian function and Taylors' theorem. In the example, a set of necessary conditions for optimal solution about the design for the minimum weight of cables with Selfweight and uniform load is obtained by using Lagrange multi plier and the above gradient expression. The proposed method shows that it is simple and efficient in solving this kind of optimization problem,including the problem of ordinary differential equations with algebraic constrains at end points.
关键词
梯度
优化
评价函数
gradient
cost functional
optimization
cable
minimum weight
