有界约束平差模型的变量代换方法  

Solving the Adjustment Model with Bounded Constraints by Approach Variable Substitution

作　　者：张立艳[1] ZHANG Liyan(Chengdu Agricultural College,Chengdu 611130,China)

机构地区：[1]成都农业科技职业学院,四川成都611130

出　　处：《测绘通报》2018年第11期83-85,89,共4页Bulletin of Surveying and Mapping

摘　　要：对于含有界约束的最小二乘平差模型,一般是采用约束最优化理论迭代求解,它要求迭代搜索方向是可行下降方向,而无约束最优化问题无需考虑搜索方向的可行性。因此,无约束极值问题的求解比相应的约束极值问题简单。本文将含有上下界的模型参数进行两种典型的变量代换,将约束最小二乘平差问题转化为非线性最小二乘平差模型求解。数值实例表明,有界约束平差模型的变量代换方法有效可行。When the constraints in least squares adjustment model are bounded,it is solved by constrained optimization theory. The searching direction is necessarily feasible and descendent.While in unconstrained optimization problem,it is not necessary to consider the feasibility of the searching direction. Thus unconstrained optimization is simpler than the corresponding constrained one. In this paper,the model parameters with bounded constraints are transformed with two typical variables substitution and the constrained least squares problem is thus converted to an unconstrained nonlinear least squares problem. The examples demonstrate that this method is feasible and effective.

关 键 词：不等式约束最小二乘 有效集方法 反正切变换 正弦变换 非线性最小二乘 

分 类 号：P207.2[天文地球—测绘科学与技术]