齐次约束的切平面近似及在优化设计中的应用

Tangent Plane Approximation of Homogeneous Constraints and Its Application to Optimal Design

Nearly in all linearization approaches nonlinear contraint functions are approximated by the linear terms of their Taylor expansions.If the expansion point is not on the constraint surface,this method of approximation would produce appreciable errors,which often cause slow convergence and sometimes divergence of the linearization approach,this paper shows that it is easy to modify the lin- earzation method based on Taylor series expansions at an approximate optimal point providing the con- straint functions are homogencous and to make the approximate hyperplane tangent to the constraint surface in order to obtain a high quality linear approximation.The examples of different types given in the paper indicate that this modification to the homogeneous constraint functions has the effect of speeding up iterative convergence and avoiding divergence.